Very reluctant when it comes to marriage advice. I'll say this though if the issue is your husband speaking with them really your family is irrelevant. Got to the source.
Husband "this isn't working when there's interference, can we please politely ask them to stick to pleasantries and no religion for a while and see if we can't just work on ourselves for a while? I care about our promise to one another and would like this opportunity.".
I agree with others in that asking them to stop will only put up red flags causing them to call into action the JW family members as they'll feel they need to attempt to get your husband to return to Jehovah.
Best to petition him Put the onus on him so that the two of you have the opportunity to make it right between yourselves.
Wish you the best.