In reality, you are being invited to a social function that your neighbors think you might enjoy. I am assuming you are friendly with your neighbors and perhaps have had cookouts/bbq's with them in the past or been social with them in some way so that this "church invitation" isn't completely out of left field. Otherwise the whole invitation would just be plain weird AND suspect (if you normally don't socialize with them).
HOWEVER, once you are at this innocent social event (Bingo, BBQ, picnic, ballgame etc...) do not be surprised if you are approached by other members of the congregation or even the minister/pastor himself and asked about joining the church on a regular basis, or about you religious affiliations etc. It may not be a "recruitment" event, but when some of the more zealous members see a new face they may strike up a religious-based conversation in an attempt to convince you how great their church is. It happens to us at almost every event we go to (here in NC you can't drive a mile without passing 5 churches...all Baptist, and they have chicken suppers and bbq's all the time which we often go to).
If your husband is uncomfortable with defending his decision to stay at your current church (or not go to church) then I would politely decline the offer, because I have YET to go to a SINGLE church sponsored event where I haven't been harangued by some member of the congregation about joining. We still go because we find their attempts kind of funny (DH and I are in a VERY good place with our faith and do not attend any church.)