I’d literally rather give birth totally alone than have a coworker there with me … that’d be uncomfortable as hell. And even if was just there for support , why would he feel the need to stay the WHOLE time ? And lie ? Red flags everywhere. 
First, how long have you been married?
Second, Could she be an ex and not just a co-worker?
Next, what’s her name and why didn’t he ever mention her before? Has he been “traveling “ much with his job?
Show up at either the hospital or work in the pretense that since she has no family, you want to help. That way it’s non-accusatory and looks like you want to help.
If he has been missing for days without calling you he might have left you. What is he doing for clothes etc…You should get your best friend and go to the hospital to find answers. You can take a gift for the mom and baby, meet her and see for yourself, and then ask to speak to him alone. Take it outside and be calm and nice. No matter the outcome you will be glad you kept your cool later.