It is possible to have both. I do think there is a risk of both the antidepressant and the stimulant to push you into mania, so be careful. Also, stimulants can be very addictive.

My husband has ADD and when he was perscribed adderal xr, his doctor told him to only take it when he needs to focus on something. And to also take "med vacations" from it, like a week or two off here and there. Because stimulants aren't like other psych meds. They don't take 2 weeks to kick in.