Can Macbook Pro handle 2.4GHz and 5GHz frequencies on the same wifi network without getting dropouts?
Chances are, it's your WiFi router.

I was having the exact same issue with 2 Macs (iMac 27 Late 2012 and a 2009 MBP) as well as a Microsoft Surface Pro 3.  I had both 2.4GHz and 5GHz networks and would get random, but continual dropouts that would lose Internet connectivity.

I disabled each network individually, first the 5GHz , then the 2.4GHz.  Running on one frequency at a time, had no effect - I still kept dropping connections.  I even completely disabled the WiFi in the router and connected another router running DDWRT acting solely as a WAP that was only capable of 2.4GHz.  Even that had problems

What I found was that the build quality of even the so-called best routers (Netgear, D-Link, Asus, etc.) were still of poor quality.  I ended up getting an "Enterprise Grade" wireless access point - the Ubiquiti UAP-AC - did my problems go away.

When I say, go away, I mean go away instantly.  From the time I installed this WAP, I have yet to have an Internet drop out.  Period.  I haven't had a single one in the month and a half I have had it installed.  The fix was instantaneous.

If you do go this route, what you will have to do is turn off the WiFi on your router and just use this external WAP.  Installation was super easy - it took about 10-15 mins total and I had my network up and running in no time.