It's very possible.
There's actually quite a lot of threads on this if you search the forums.
What it comes down to is what do you want your car to do that the B18c1 can't do and how much money are you willing to spend?
The H22a will cost you ~$2500 plus ~$650 for the H series mount kit
, plus another $500-$1000 to have it installed probably.
The motor is larger and weighs about 70 lbs more than a B series.
You can bore and resleeve the B series out to 84mm (1.97 liter?) for 1/2 as much as just the engine for the H22 would be. (about $1100).
If you plan on running Turbo you will lose your air conditioning and it will be hard to keep your power steering. I'm not sure but you might even lose AC with a non-turbo application, because the engine is so large. There's some people trying to develop ways to keep these options as we speek, but for now that seems to be how it is.
My own opinion? Don't do it. Keep the B18c1 & spend the $4000 tuning it, or boosting it (whatever you prefer.)
The USDM h22a is only 25 more horsepower than the B18c1.