You can't lose your fat because you're eating too much. Gaining mass requires a caloric surpluss or caloric balance. I.e. you eat more than you need so it gets turned into muscle with the bit of left over converting to fat, or you consume just the right amount and you gain only mass with negligible fat. To cut fat, you need to eat a caloric deficit. I.e. you eat fewer calories than your body needs to function so that it is forced to use stored fat for energy. So, it's very difficult if not impossible to continue to gain mass while cutting fat.
People often look bigger after cutting fat, and they may think they've gained mass, but it's an illusion. Their current muscles are just showing through.
So I imagine you're just eating too much. Your body doesn't need to burn fat, so it isn't. It doesn't matter if you lifted weights non stop for the rest of your life while continuously running like Forrest Gump. If you still ate too many calories, you wouldn't burn the fat
My advice would be to alter your diet. Use the Harris Benedict Equation to calculate your needed caloric intake to maintain your current weight, then knock off 500 to 1000 calories daily. Keep up your lifting routine, do hiit a few times a week, and cardio if you have time. And make sure you eat enough fruits and vegetables. Your carbs should primarily come from these except right before and after a workout.
As for HIIT, 5 min warmup, then either 30/30 on/off or 30/60 on off if you can't handle it to start. begin with 5 minutes, so 5 cycles of on/off. 5 min cool down. Your goal should eventually be 15 min of on/off cycles. Of course if you can do more than 5 minutes from the get go, by all means, go for it.