Your healthcare at work is paid from your wages OR by the company and is recorded on your W-2 in Box 12.
Obamacare/ACA is usually paid (at least partially) after-tax or by money "out of pocket". That is why you receive the Form 1095-A and should input that only for her.
You may receive a Form 1095-A or Form 1095-B from your work showing you were covered by insurance but you do not have to enter that on your return. Just your wive's Form 1095-A.
