This very much depends on the wording of your invitations but also your relationship with your parents.
For example, if your invites say something along the lines of; Mr and Mrs Nguyen request the pleasure of __________’s company at the wedding of their daughter etc…
It’s going to look a little strange to say; Mr and Mrs Nguyen request the pleasure of Mr and Mrs Nguyen’s company at the wedding of their daughter etc…
Since you are paying for your wedding, I assume this isn’t the case, but even if your wording uses yours and your partner’s names to invite your guests, on your parents’ invitation, you should use whatever terminology you normally use when addressing your parents face-to-face.
I’m a big fan of ‘Mum’ and ‘Dad’ because that’s what I call my parents.
I don’t see the point in changing that merely because invitations are, traditionally, worded quite formally. It’s the equivalent of calling them ‘Mother’ and ‘Father’, which sounds contrived unless that’s what you usually call your parents.
So, I’d recommend using whatever name you naturally call your parents is best, even if it’s a nickname such as Pops or Mumma. After all, you’re essentially saying, ‘Mum and Dad’ please come to my wedding,’ aren’t you?
Of course, if you’re not comfortable with that level of informality on your invitations, you can always use the Mr and Mrs honorifics but the way to find a solution that won’t be awkward is simply to imagine you’re sitting in front of them and asking them to come to your wedding.
How would you address them?