Yes, it's very possible, but it doesn't seem to affect all couples. My hubby and I have been together for the last 18 years, and although he did get infected (he's had plenty of ticks to do this), he was treated fast and properly, and he's not had any other issues since. We do not use protection in the bedroom (hubby refuses, even though he knows the risk).
Lyme is something that I don't seem to "share" well, as I also carried my kids while infected and untreated/undiagnosed and they have not had the symptoms either. But let me get a cold or flu and I share that with everyone!! LOL!
If your hubby has been infected for quite a while, it's possible that he won't test positive no matter what testing you do. Lyme lowers the immune function, and these tests all rely on a well functioning immune system to produce the antibodies that the tests all look for. PCR testing has it's issues as well, as not many will get a positive if only low levels of bacteria are causing their illness - which is fairly common.
You can have him take this questionnaire to help determine if he should get tested or maybe just trial some herbs (if he's
open to that):
lymeontario.com/wp-content/uploads/2015/03/Horowitz-Questionnaire.pdf It will at least give you a little better understanding if he needs to be tested.
Herxing is often very misunderstood and many that try to use abx for this or that when they have Lyme unknowingly, will then assume they have an allergic reaction, when in reality it's herxing. Just be sure that if you choose to try something to watch out for signs of a true allergic reaction and act promptly should it happen. I like to have Benadryl on hand.