not knowing the US citizenship status of you or your husband, it is hard to answer your question definitively. But I live in a border state (Arizona) and have been through those checkpoints many times. Even regular US citizens can sometimes be asked to get out of their cars once in a rare while.

What I would recommend is this:
1. if you or anyone in your party is not a US citizen, you should be prepared to show your passport.
2. if someone in your party is a legal US resident, then just your US driver's license should be sufficient
3. when you approach the checkpoint, take off your sunglasses and roll down your windows.
4. don't do something stupid like my DH did a few months ago and pull over in sight of the CBP agents to rearrange your luggage in the back of your car. You will get your car searched for surr.
5. If they ask you any questions, just answer calmly and truthfully and you will be fine.

A close friend of mine works with CBP agents on a daily basis. Here in arizona, the border patrol has caught illegal immigrants from many countries who harbor terrorists. Plus there are Mexican drug cartels who fire weapons at the CBP agents in their vehicles. So if the New Mexico CBP agents seem especially vigilant, there is a legitimatr reason why and they are not necessarily singling you out for discriminatory purposes.

For example, a couple of weeks ago, I and my family passed through such a checkpoint while driving from CA to AZ on vacation and the CBP agents asked me if I and everyone in the vehicle were US citizens.