For Byzantine History there simply isn't a comprehensive history of the Empire that's really thorough. There are books that certainly try, such as the first book I read: The History of the Byzantine State, but even that 500 page book felt awfully rushed at times. If you're interested in reading about Byzantine history, I recommend you do it segmentally, reading the books on particular periods before moving on. In my opinion, the best books to do this with are recent and good translations of the primary sources, as these will hit the major events of each emperor's life while a good translator will have thorough citations noting where things are wrong, where you can find more information on a particular topic, and where the sources disagree and we don't know what exactly happened. John Wortley, for example, did an excellent translation of the chronicle of John Skylitzes which covers the middle Empire from the death and drinking cup-ification of Nikephoros I and ends with the ascent of Isaac I Komnenos.

I haven't read the book you mention but I cannot recommend highly enough The Hollow Crown by Dan Jones for the Wars of the Roses.

I also suggest that before that you read The Plantagenets by the same author, they go very well together. The Plantagenets is probably the best history book I've ever read and while its focus is much wider than Henry II/Richard I, all that stuff is covered and it really is a terrific read. I absolutely blitzed through that book.

1. You can't really go wrong with W.L. Warren, 'Henry II' (Yale English Monarchs, 2000), as a starting point for Henry II. It's old, but (very) comprehensive and although I can't remember the specific parts which deal with the family conflicts, I'm sure they're in there.

2. Not really a Byzantinist, but I don't think I've ever heard of a good book which covers the entire Empire, other than John Julian Norwich's trilogy ('The Byzantine Empire'), which is very old and dated. I read Michael Angold, 'The Byzantine Empire, 1025-1204: A Political History' a few years ago. It covers the central period (which I was most interested in) very well, especially relations with the Latin West leading up to the Fourth Crusade. Brubaker and Haldon's 'Byzantium in the Iconoclast Era' is, I've heard, the authority on the earlier period of Byzantine history: I havn't read it, but I've read other things by both historians and they've been excellent, so I don't see why it wouldn't be. If you're interested in the Byzantine role in the Crusades, Peter Frankopan recently wrote a book (I think it's just called 'The First Crusade') which really puts the spotlight on the Byzantine role in it all (I havn't read it, but saw him give a talk on it and it seemed like and interesting angle).

I don't know much about the War of the Roses period, sorry.

Just a quick note that most of the books I've listed above are more academic in tone than Asbridge's 'The Crusades'. Not that one style is better than the other, but just to be aware of the different styles (for example, Warren's book on Henry II is arranged thematically, rather than chronologically, IIRC.)