Tell him to catch one for identification.

Most spider bites leave a big itchy welt.

If you vacuum thoroughly (floor, wall corners, etc), and dispose of the bag immediately you can minimize the population.

Consider bedbugs - they hide in craclks in the walls and furniture during the day.

sounds like bedbugs. They only show up in the dark and find people by smell/heat. I found one in our cabin which was dead under the mattress pad. I looked them up on the internet.I used borrax along the walls in the bedroom after I vacuumed for a long time. My son complained of bites when he woke up the week before I found it. I don't know where they came from but they were not welcome to stay. Be generous with the borax and let it stay for as long as you can. They have to walk in it to die. You can buy it along with washing soap.

I'm afraid that you're probably right -- after some more research, it's probably bedbugs :( :( We're getting bit at night, and while sitting on the couch. I've already done an extreme cleaning of the bedroom, and it doesn't seem to have helped much...and I don't even know how to clean the couch with all it's crevices. I guess we're going to have to get an exterminator.