I met my DIL's parents at the wedding, and haven't seen them since. My son has arranged a big night out in the Spring - we are going to a gig then staying in a hotel - us, the ILs and the 'children'. I'm looking forward to it, but don't expect that we will all become firm friends afterwards. Who knows though?
We live in different places, so the distance would make it difficult. They are 10 years or so younger than us, and still work, and we don't (on the face of it anyway) have more than the children in common. The connection is that they brought up the woman who makes my son happy, so on that basis I like them.
My parents and my ILs were the same - friendly and relaxed in one another's company, but not 'friends'. They sent Christmas cards, but didn't visit or otherwise socialise - why would they? I suppose in the days when people all stayed in the same street it was different, but these days that's relatively rare, I think.