Are his books a reliable source for those looking for the basics of Western history?
Isaac Asimov produced an enormous amount of material. He wrote hundreds of books, thousands of stories (and some pretty terrible limericks), and put his name on at least as much stuff that he didn't actually write or edit. It would be difficult (and tiring, given his rather unimpressive, if lovable, style) to go through the entirety of his written work, or even to analyze systematically only his fourteen pop history books, to which we might add his companions to the Bible, Shakespeare, and other literary works, and even perhaps his autobiography. Let it suffice to say that his history novels are, were, and no doubt always will be totally ignored by serious students as actual pieces of scholarship, or even as examples of popular history. Isaac Asimov had a great deal of interest in the history of the world, as he had in just about everything else: how well he understood the history of the world is a completely different matter. His histories of Rome are pretty indicative. They rely extensively on Gibbon (already discarded as a scholarly work for over a century by Asimov's day), from whom he took much of Foundation, or consist of a series of amusing stories (which may or may not actually be in the texts), ideas outdated already in Asimov's time, or sometimes Asimov quite clearly leaving his historical setting and talking about his own ideals. His The Roman Empire, for example, while careful not to endorse Gibbon's really rather silly attribution of the end of the Empire to Christianity too strongly, is in large part pretty clearly a polemic along the lines of some of the stuff in his enormous autobiography. Which is not to say they're not fun. They're enjoyable to read, if you can stand that much Asimov, and he treats the stories as stories--truthfully I don't think he could've given less of a damn about the actual history. Like so much that he wrote he seems to have personally enjoyed writing his histories, but as real primers of history? There are much better options.