The first time I tried to follow the program, I felt like you, breathing really really hard. I kept going anyway, but I could only complete the program until week 5. This year, I tried again and the first week was a lot more manageable, because I was in better condition after building it up with hikes and walks with the dog. You should not be gasping for breath, or be unable to speak.
If the first week is too hard for you and you find yourself gasping for breath during the running portions, IMO you should try to build up your physical condition first by walking, hiking, biking, swimming, etc. Aim for 30 min walks, then increase the time to the point when you're not breathless at the end. Try speed walking, hiking, etc. After about 3 or 4 weeks you'll be ready to go back to week 1 of the c25k program without risking a heart attack. Take it easy, it's best to build up your strength slowly than to give up by week 3 and feel like a failure. You wouldn't be giving up, just starting from another point. The important thing is the decision to exercise and be healthier. Good luck to you and your husband!