Eating shouldn't be an either/or activity, but you're right to question the items and the timings.
You should be looking for something slow release before - so the fats in a muffin combined with the slow release carbs in the dough are cunning (my favourite is a jam sandwich - fast release fructose from the jam, inhibited a little by the fat in the butter, with the slow release from the bread kicking in later). It's the morning, so maybe a milky, sugary coffee could be in order!
Then remember to refuel during, quick release, so gels or powder in your water bottle are great.
Don't overlook the recovery mixture. Your body is in heavy replenishment mode for 20-30 minutes after a workout and will be looking for proteins to help muscle recovery as well as new sugars to boost the blood sugar for the day ahead.
Interval training will strain the body more than long, slow, distance, so you'll definitely want to look at the refuelling strategies (you can buy specific post-exercise energy drinks).