I printed these over the summer for a lovely couple from Berkeley. I letterpressed the invite and rsvp cards and they screenprinted the envelope and digitally printed the enclosures themselves. I think this is a great way to create an invite if you're hands-on like they are or are on a limited budget but don't want to lose any of the beautiful details of your design. If you're crafty enough, there are many ways to make a set look cohesive without having to letterpress each piece. I encourage you to talk to your printer and ask advice on different options--mixing printing techniques isn't against any rules of etiquette. I think if anything, it gives it a lovely, handmade look when done right like Kelly & Eddie's invites. You can definitely tell when something is made with TLC :)
These enclosures were printed on their inkjet--it's impossible to match inkjet colors with real pantone inks but I think these are pretty close.
They used a home screenprinting kit for the envelopes. I think these gocco sets are discontinued but another way to get a similar look/feel is by getting a custom rubber stamp made of your image + return address.