Hiit vs running and doing both

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Hi everyone,
I'm new to this community. I've been working out, running, eating clean (for the most part) for about 3 years now. I really enjoy running, I run about 6 miles 5 days a week. More if I'm training for a half. I really want to start focusing on building lean muscle. Everything I read says to do HIIT's vs steady cardio. I guess my question is can I do both or is that too much? I don't want to give up running. I work 3 nights a week, 12 hour shifts. My first night of work I run before work, then I don't work out for two days, then after my 3rd shift I sleep a few hours and get up and run and either do insanity or a daily hiit from bodyrock. I'm not really seeing any results lately, although my diet hasn't been the greatest so the last week I've really been focusing on cleaning that up. Any tips or suggestions on what would be best to build lean muscle and get rid of this little stomach pooch. How many hiits should I do a week? Weight training, running, etc? I guess trying to fit it all in is what is confusing me. Thanks