It is very cool...
...that you adore your parents, and presumably they adore you. If you guys really have a positive relationship, how could you not miss them?
Insofar as me and my mom, we have a very love / hate relationship. It is NOT as functional or healthy as I would like, but I long ago realized that she wasn't going to change, that it was up to me to simply draw the boundary lines. My mother grew up in an era / culture where parents related to their children in a certain way, and that way doesn't work for me.
In a way it makes me sad...because when I was growing up, my mother and I were WAY CLOSE. VERY CLOSE. Everything you'd expect in a positive way from a single mom and her son against the world type of situation. I was amazed when people / friends would talk about their relationships with their parents, when I knew I could talk to my mom about anything, and did. We spent hours just talking...car rides...listening to her old Motown records.
Even when I became a young man, my mom and I were still pretty cool. We'd go out for dinner, things like that. She was so proud that her son could afford to take his mother out to a fancy restaurant...lol.
The split started my senior year in high school, when the time to go to college came around, and my mother didn't support me. She just had no reference point...she hadn't gone to college (how ironic that later I would SEND her to college, and she would go on to pursue a Ph.D), and everything she heard from the "white folks" at work was that kids went to college and fucked off, wasting their parents money. There was no telling her I was different, that I was a (relatively) bright and gifted student. I couldn't convince her, my high school counselors couldn't convince her, the counselors and leaders of the special program I was in for gifted minority students couldn't convince her. Things got so bad that I actually moved away from home before I graduated from high school...and only saw my mother again at the graduation itself, and when she helped me move into the dorms at university (I am sure she couldn't believe I really had managed to get in and go without her help). I sent myself to college, my own dime, with very little contact and support from her.
The split widened when I was going to graduate...and for no reason other than spite (IMHO...she denies it)...my mother refuse to come to my university graduation. She just wouldn't admit that I had done it.
We recovered from that, and had several good years (the years I was sending her to school), but another split came when she took things for granted regarding how I was going to support her Ph.D aspirations. It was an ironic twist, though it was more complicated than that (some personal family stuff and history that came to a head).
That got patched up after a period...some more years of things being keen, culminated with me bringing her to Canada to be closer to her grandson.
Currently, there is again a rift. She isn't happy about having come to Canada, only to have the ex and I split, and she have to return to the U.S. and try to restart her life. I don't blame her, to be honest, but I have my own shit I am dealing with, so I've only got some much bandwidth for sympathy...
This will pass too, with time.
Anyway...all that to say...be glad you have a positive relationship with your folks.