Putting a Cat and a Dog Together

How do you get a four-and-a-half-pound Burmese (who will be 18 in December) to co-exist with a twenty-five-pound Miniature Labradoodle (who will be four years old the end of this month). Ever since my husband and I got married more than a year and a half ago, we have kept our pets in different areas of the house; because my husband is afraid that my dog will harm his cat. However; when put together (for a brief period of time), the cat hisses and the dog starts to shake! The cat is afraid of people; whereas the dog will greet strangers with tons of affection; i.e. kisses. Help!

Okay, here we have a cat who knows the dog COULD be a danger, so he's hissing pre-emptively. Hissing is a warning of "If you're still here is 2 minutes, I'm going to jump you & rip you to shreds with my claws". It's totally normal, & usually doesn't deteriorate into a fight unless the other animal pushes the issue. The cat may be afraid of people, but dogs, he can handle - especially small dogs, & he's warning this one not to try anything.
   
Your dog is apparently a very sociable, peaceable creature who absolutely blanches at the thought of an angry cat. And he's not much bigger than the cat (that's a REALLY small Labradoodle.) (And a really small cat, come to think of it - only 4.5 lbs? Wow. He's real runt.)
   
This is not a totally bad situation. The dog isn't interested in attacking the cat, or he wouldn't shake. He's downright terrified of the cat - after all, he probably only wants to be friends, so WHY is this tiny furry creature cursing him out?. (Is his tail wagging & his ears standing up straight when he meets the cat, before the hissing? Then he's being friendly.)
   
I suggest you give them supervised time in the same room, every day, over however long a time is necessary to settle the relationship down. You have to get past the "brief period of time", which is always the most tense - neither has gotten past the Initial Hostilities stage.
   
Start with an hour, then up it to a couple of hours, then lengthen it to large chunks of the day. Just make sure nobody jumps anybody else (in this case, I think the cat is more likely to attack - which is rather funny, as your husband was worried about the cat, not the dog).
   
Once the cat figures out that the dog isn't a real danger, the hissing will stop. When the dog isn't being hissed at anymore, he's stop shaking & probably try to introduce himself. At that point, the relationship will even out into anything from guarded neutrality to actual friendship - there's no way of knowing where it will land. If the cat is truly against the friendship, the dog may get his nose whapped, but it likely won't be too bad, & likely won't involve claws.
   
You might also want to try Feliway, to relax the cat a bit (a pherome-based tranquilizer for cats). Spray it on the cat about 15 min before you put them together, & spray it on the dog, also. It won't directly affect the dog - you just want the dog to smell calming, so to speak, to the cat.
   
This is far less complex than it appears - in fact, it's ridiculously normal - , & your husband is way more worried than he needs to be.