I sympathize, as I can be like that too, falling asleep in the car and DH has expressed that he gets annoyed by it and I've told him "Look, I get sleepy in the car, and even more so if I don't have a reason to stay up, such as carrying on a conversation. If you want me to stay up, I will try but it helps if you'll hold a conversation with me. Otherwise I just assume you're bored if all I'm getting is "Mmm-hmm", "Yeah", "Uhuh" or just facial expressions."*
*My mother once told me that those sorts of responses can be a cue that people aren't interested in what you have to say.
He has become more talkative in the car on long trips so I think he got the idea.
On the other hand, once I was in the car with my best friend and I think she could tell I was tired and kept encouraging me to take a nap but I felt weird doing so and ended up nodding off on the couch once we got back to her house (was staying with her for a week)
Caffeine might help, or an energy drink...or just more sleep.