I worked for the PO for 14 years. I started a year out of high school as a substitute rural carrier, and 9 years later, I got my own route. I left almost 4 years ago, because I got Rhuematoid Arthritis.
I will tell you, it is VERY difficult to get a job with the PO today. they are not hiring really. The PO has one of the best Unions, and as of 4 years ago when I left, there was no such thing as lay-offs. They have offered early-out retirement packages, to get people to leave. So, basically, you have a place that needs to cut back on the labor, and can't. So, they shuffle people around, and don't hire anyone new.
They'll always need carriers, unless they have robots do it. But, they hire within, and there is always someone willing to step into a full time position.
If your Dh does manage to find a place giving the postal exam,( I haven't seen an exam open to the public in years) and they are hiring, he should expect to work part time for a few years anyway.
Good luck. I was very fortunate to work for the PO.