Turn the tables. Imagine that your husband had some concerns about your child's development or health. Nothing critical, but something where infant/toddler development of a parent might help influence decisions and he feels like he has enough information about his own health history that his past is exempt from analysis. For example, you child has chronic ear infections and he knows for a fact that he never had one, but you have had a long history of allergies and sinus problems.
So your husband wants to get information on your history of ear infections but you think the baby is in the range of normal (as in you don't have to decide TODAY whether or not to have tubes put in) and you're super-stressed about something else right now and this can wait a few weeks or a month until you're done with your big project (or holidays or whatever the stressor is).
So then if you found out that your husband did an end run around you, went to your mom and asked her to keep his inquiry a secret, wouldn't you be beyond livid?? If course you would be! Because you're probably thinking that you husband is being invasive, crossing boundaries, disregarding your take on the situation, and questioning your parenting skills.
I'm sorry, but what you did here was very wrong. If you child is in a spot where you need medical records and information to make critical decisions regarding his health *TODAY* then you should have gone to your husband and insisted on him calling his mother to get this information. If you didn't do this because you didn't want to bother him, then it wasn't all that critical. This could have waited until his finals were over, you were just being impatient and want to know what you want to know right now. I can be that way too, so I understand. I want to turn over every rock, investigate every angle, especially when it comes to my children but the way you went about this was just all wrong.
Apologize to your husband, admit that you were wrong. Then tell him that you did what you did because you are concerned about your son and want to put your fears to rest and feel that knowing his developmental history will help you to relax and allay your concerns, so you would like him to please get some information from his mother when his finals are over.