Re: is it...healthy?
Baby is an affectionate term, used when you are romantically attached.
I am suspicious, if it's in the past why hasn't he erased the emails? If he is your fiancé why hasn’t he been open and honest about his past relationships? It’s a question of sincerity and fidelity.
If the issue is playing on your mind it should be discussed to erase your doubts. If he’s avoiding the conversation then this will make you suspicious.
Forgive him about his past misdemeanours. However trust may only take a moment to break but much longer to regain.
You fiancé is rather inept, he should have erased the emails long ago.