I would not do HIIT every day. And I would never do it for more than 15-20 minutes. In fact if you can do it more than 15-20 minutes then you are not doing HIIT properly.
Here's a bit of a better schedule using the one you just provided:
Do a 5-10 minute cardio warm up.
Do your strength training session.
Do 15 minutes medium intensity cardio.
Cool down and stretch.
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The difference between HIIT and Interval Training is quite large. HIIT is walking for a minute, then sprinting all out oh my god I cannnot believe I am going this fast for one minute, then walking for one minute, then sprinting all out oh my god I cannnot believe I am going this fast for one minute, then walking for one minute, etc for 15-20 minutes. This should NOT be done on a day that you do lower body strength training, it should NOT be done on a day after lower body strength training.
Interval training is one minute of this, one minute of that, one minute of this, one minute of that for as long as you want to go (no more than 45 minutes). It may include medium intensity and higher intensity levels, but it is not the same at HIIT.
I don't want to make this sound complicated (am I failing miserably at that?), but it isimportant to workout correctly... especially when just starting out. And I wouldn't keep all your cardio in 1 zone. Your body will adapt.
I would mix up my cardio each week to include a few medium intensity and session length days, 1 long session, low intensity days and maybe one HIIT if you are in shape enough.
is a good read and supports Malkore's post. Which I agree with (aevans410 postas well).