Newbie runner

If you haven't been yet, sometime within the first few weeks you'll want to get fitted for the proper shoes at a store that specializes in running. You can get away with any old shoe while you're still doing mostly walking but you'll eventually need a good running shoe that helps with the way you run. They also need to be 1/2 to 1 size larger than you would wear for every day, something I learned the hard way.

Don't run more often than every other day. The recovery period is just as important as the runs themselves. Follow a structured plan that has rest days every other day and slow mileage increases built in. Running is tough on your joints and your body needs to rest so avoid other high impact activities during this time. If you would like to stay active on the days you aren't running then walk, bike, swim, lift weights, etc.

Don't worry about breathing. Mouth or nose doesn't matter, it's all in what is comfortable for you. However, if you're getting out of breath while running you're probably going too fast. You should be running at a pace that is slower than you'd imagine "running" to be; one at which you and your husband can carry on a conversation. It's not speed you're after at this point, it's endurance so don't judge your progress by how fast you can go but by how far you can run without stopping. Speed comes later.

Your strides should be very short. Your foot should land nearly under your body. This will help you avoid over-striding which leads to injury. Elite runners are advised to take 180 steps per minute. While you're just learning and still going very slowly you'd probably be looking at 160 SPM (right and left each count as one). I actually used a metronome app to count off 180 SPM for me when I was finished with the couch to 5K app and working on more speed. It's so engrained now that I run at about that cadence regardless of what music I'm listening to or how fast I'm running.

Most of all, have fun. I think it's awesome that you two are doing this together. You'll keep each other accountable and running is always more fun with a partner.