Anything's possible, but "possible" and "a good idea" are two different things. You would need to also put in the engine computer from the Honda, and either include all the accessories (air conditioning, power steering pump, etc) from the Honda or figure out how to make the Cavalier accessories work with the Honda motor.
You don't say whether your Cavalier is an automatic or a manual transmissioned car, but either way, mating the Honda engine to your Chevy transmission or transaxle would be quite an engineering project.
Then of coure, you'd need some exhaust tubing fabricated, 'cause the Honda's exhaust manifold probably won't match up to where your stock exhaust pipe begins.
There's also the matter of having motor mounts custom fabricated.
And don't even get me started on the nightmare you're going to have when you attempt to get this thing to pass a smog check.
The real question to ask is, why do you want to do this? If it's more power you're looking for, you'd be better off purchasing a new Chevy engine for your Cavalier and adding some smog-legal performance upgrades to it.
If reliability is the issue, I think a new or rebuilt Cavalier engine is going to give you far fewer headaches than you'd have if you cobbled together a Chevy/Honda Frankenstein creation.