That's an interesting question. In the case of the Western Front, it's a pretty straightforward answer at first: trenches were generally assigned by sector, so you'd have a chain of command of your own national army in charge of one particular section of trench, and you'd have other national armies at your side. This formation was remarkably well-preserved due to the static nature of trench warfare, and as a result, Allied commanders would generally find themselves serving among other units of their own army. Here's a map of a 1915 battle to give you a better sense of what this would look like - note the Germans have unity of command, while the Allies are divided primarily into three sectors of their front line. https://fffaif.files.wordpress.com/2009/07/fromelles-map-7_sml-location-of-armies-on-the-western-front-30-june.jpg

When the Americans joined the war, there was contentious debate on where to put those reinforcements. General Pershing, the commanding officer of the American Expeditionary Force, insisted that Americans be led by American commanders, but the exhausted French and British wanted them to fill gaps in the depleted Allied lines. Pershing's insistence meant that only 14,000 American troops were in France at the end of 1917, and precious few had seen combat. In order to compromise, Pershing agreed to allow some units to serve under French and British commanders, on the condition that every American unit arriving thereafter would serve under US officers. For the first half of 1918, therefore, most action in which the Americans fought was under the ultimate command of French or British officers, and it wasn't until the battle of Saint-Mihiel in September of 1918 that a large scale American army went into action on its own. The American case, however, is the exception to the rule - by and large, combatants on the Western Front stayed within the sectors administered by their own army.