Yes, it is possible for a person to have a negative Celiac blood test panel but a positive intestinal biopsy for Celiac.
Celiac genes are not the only genes involved in whether one can tolerate gluten or not...there are also Gluten Sensitivity genes. See www.enterolab.com/
for more info on Gluten Sensitivity.
Your Husband is clearly Gluten Sensitive, if not full blown Celiac, with those saliva test results...and he probably would experience improved health on a gluten-free diet.
Your symptoms with your genetic predisposition for Celiac speak loud and clear that gluten is an issue for you, whether or not you actually have Celiac. If I were you, I'd stay away from gluten!