/u/Cutlasss is absolutely right that it depends, though I would approach the question differently: What do you mean by "healthy"? If you mean healthy according to today's standards, then probably "yes." Today's food has a lot of nutritional governance and intervention built into it, and the bodies of knowledge that guide that intervention include nutritional science, the very science that determines what "healthy" food is. It follows, then, that food would be "healthier" according to those metrics. So, for example, the flour in most bread is "enriched," with various minerals and vitamins added to highly refined white flour. These materials restore or even surpass the vitamins and minerals in whole meal flour, materials that are removed in the process of creating white flour. Now, certainly people can and do argue against this, saying that this is "unnatural" or that people should just eat whole wheat flour instead, but the bottom line is that by the metrics deployed by nutritional science--quantitative measurements of calories, vitamins, minerals, etc.--the current flour we eat is perfectly healthy if not even more than it was in the past. This is true of many other products: milk is fortified with vitamins, infant formula is far and away better than it was a century ago. Food today is also probably more "pure" than it was in 1914, but I should stress that by that point purity and adulteration were nothing like the problems they had been in the middle and late nineteenth century. If you and I went back in time to 1914, I wouldn't worry too much about the food; if we went to London or New York in 1850, then I'd worry quite a lot.

However, it is important to recognize that there are now and always have been disagreements within nutritional science and medicine more broadly about just what comprises the (or an) ideal diet; that's the "Omnivore's Dilemma" that Michael Pollan identified and has made a career writing about. In terms of the history of nutrition and food, food's health values have always been open for debate. And, in a general sense, we know that people in the West, and much of the developing world besides, are in some ways less healthy than they were in recent decades. Diabetes is rising, linked to our large consumption of refined starches; the major processed food companies have been implicated in this for creating "low fat" or "low calorie" foods in which they removed fat and replaced it with sugar and salt. There was certainly a substantial period after the Second World War when fats in foods were seen as major problems, a view that has been called into question. This ambiguity in nutrition makes it difficult to assess whether or not food is "healthier" now than then, because the standards for what constitutes healthy are always changing.

But, there are some important changes that we should note about societies' diets. The most fundamental way that things have changed, and in my view improved, in the past century is that people in the West, by and large, have a diet sufficient to maintain health. Today, people get enough more frequently than they did a century ago. In Britain, at least, hunger and very meager diets were relatively common in the years before World War I; the 1904-5 Inter-Departmental Committee on Degeneration found that many working class Britons lived on a diet of bread, jam, and tea, children in particular. Their only protein sources were fried fish a few times a week, and the only vegetables the occasional friend potatoes. Many working-class women before 1914 did not--probably could not--breastfeed, due either to the need to work many hours away from home or due to their own poor nutrition. Infant formula being too expensive, their children were fed a kind of broth made from boiling pieces of bread, and then bread and tea as soon as they were old enough to chew and swallow. This led to much higher rates of infant mortality and deficiency disease. Floud et al.'s recent work The Changing Body makes clear that people have gotten substantially taller across the twentieth century, reflecting the poor diets of the early twentieth century. Derek Oddy's From Plain Fare to Fusion Food, the essential monograph on the last century of food history in Britain, pulls together a considerable body of research finding that Britain only began to get enough to eat, so that hunger became a much reduced problem and deficiency diseases almost nonexistent, during and after the Second World War.

In addition to amount, our diets today are far more diverse than they were a century ago. We have considerably greater access to fresh produce year-round, protein sources like fresh eggs, milk, cheese, and meat. Of course, now as then, access to fresher food is dependent on one's position in society: many poor urban areas today are described as "food deserts" for their lack of food provision options. However, there seems little doubt to me that access today is more widespread than it was a century ago; it is broadly cheaper and more diverse.

An answer to your question becomes more interesting if the date gets pulled back a little (or a lot). As /u/agentdcf has mentioned, food 100 years ago was probably ok, if not that varied. Go back another 50 years or so and the picture changes considerably. The food commoners ate at that time was probably not always ok, but more importantly it was extremely one sided and therefore often lacking in essential nutrients.

Peasants in northern Europe were reasonably well off: they almost exclusively ate potatoes. While that is a very boring diet, it's not actually that bad from a nutritional point of view as potatoes have quite a bit of vitamins and proteins in them.

Peasants further south, however, were off much worse. By the 19th century corn flour (polenta) had become their staple diet. Unfortunately the nutritional profile of corn is very, very poor (unless you supplement it with beans, as was done in the Americas) so diseases like pellagra were fairly common in Italy and the Balkans.

For the middle classes, the picture was somewhat rosier as they had access to a larger variety of foods, albeit often of fairly dubious quality. Poor people, also those living in the cities, however, had truly terrible diets.

If we go back even further in time the picture changes and surprisingly enough it's the wealthier city dwellers that become worse off: the foodstuffs that make it to the cities are often spoiled or adulterated (cutting wheat flour with chalk was a common practice) but peasants actually eat reasonably varied diets. The staple foods (things like rye, barley and other supposedly second rate grains) are still nothing to write home about, nutritionally speaking, but because there's a larger amount of land that is uncultivated, they can supplement these with foods foraged from the wilderness.

The further back in time you go, the larger the part these foraged foods play in European peasant diets becomes. By the time you're in the sixth or seventh century AD, you'll actually find that peasants (meaning mostly everyone as there are only a few very small cities in Europe at that time) eat reasonably well. They supplement their (admittedly meagre) grain rations with wild game and other forest products and when the grain runs out they start eating chestnuts and even acorns, which may taste terrible but which are actually not all that bad for you.

Of course, once those run out they start starving. You could therefore summarize the food situation for medieval peasants by saying that they have fairly good food, just not that much of it.

TL;DR In general you could say that nutritionally speaking the quality of the food available to common people of Europe has steadily declined since the fall of Rome and hit an absolute low point at about the end of the 19th century.

Source: Massimo Montanari, La fame e l'abbondanza: Storia dell'alimentazione in Europa (sorry, I was unable to find out whether this book has been translated into English. I read it in Dutch).

I would like to see someone knowledgeable take this question back an order of magnitude or so. I've frequently heard about "Paleo" diets being all the rage, since before agriculture, a person's diet must have been 'natural.' I know someone personally who is trying to eat in this way. It looks like madness to me, but is there any validity?