Not without his authorization. Inmates retain the same medical privacy rights as anyone else in the healthcare system. Marriage does not automatically grant a spouse access to another person's medical information. The facility will not release details about why he was sent there, what treatment he received, or what his diagnosis is without the proper documentation.
The two ways to get access are a signed medical release form from him authorizing the facility to share his health information with you, or a healthcare Power of Attorney that grants you legal authority to receive medical information on his behalf. Either document has to come from him voluntarily. If he is unwilling or unable to sign, the information stays protected.
If you are his spouse and genuinely concerned about his health and future care, the right conversation to have is with him directly. He can choose to share what happened, sign a release form so you have access going forward, or designate you as his healthcare decision-maker through a Power of Attorney if he wants you to be involved in his care. None of that can be imposed on him from the outside, but all of it is available if he chooses to put it in place.