From what I've found it should be possible and here is how:
On PS4, you can see your PS3 friends in the main PS4 menu, and can see that they are playing Helldivers. Inside Helldivers, on the "Friends" screen you will see that your friend in Online, but it will not show their helldivers game info by default. Highlight their name and press square to see their Helldivers info and then you can join. Every now and then I get "Teleport boot failed" when my friend is on the bridge and I have to wait for them to start a mission before I can join.
From PS3, it's very similar, but you can't see if your PS4 friends are online from the XMB (unless it's changed recently). When you view your friends list from inside Helldivers, I don't think you see the PS4 friends as Online, but press square and the info will show up.
Hope this works for you