Tube-based integrated amplifiers are readily available. They combine a preamplifier and an amplifier in a single chassis. The ones I'm aware of are two-channel designs, though, not multi-channel home theater systems. A Web search should locate some of the companies involved in this market. You also can get more information about them in the two-channel audio forum: http://www.avsforum.com/f/173/2-channel-audio
Of course, using separate preamp and amplifiers is more flexible. You can upgrade either without changing the other. Separates do tend to be more expensive than integrated amps.
Personally I don't have any tube electronics any more (not for the past 30 years or so
) so I can't make any specific recommendations. My impression from recent articles and advertisements I've read is that modern tube designs are rather expensive, primarily because the market is so small, so they don't have the advantages of the cost reductions possible with large production lines. Finding the right tubes for use in older devices can be a challenge, too.
Don't forget that, among other sophisticated features, modern solid-state home-theater receivers include room equalization software, which can compensate for infelicities in speakers and room acoustics. Tube amps can't do that at all. Treble and bass adjustments are about the limit for them. Of course, they can't decode any of the modern digital audio soundtracks either. Decoding digital audio into analog signals for use with tube electronics has to be done in the player. Disc players with quality analog outputs are rather expensive, too. They start at about $250 (Panasonic) and go up. Way up. Oppo players are about $500 or $1000 depending on the model.
I hope these comments help a little.