It looks like you're using the wrong tool there. Grep isn't that sophisticated, I think you want to step up to awk as the tool for the job:
awk '/blah/ { getline; print $0 }' logfile
If you get any problems let me know, I think its well worth learning a bit of awk, its a great tool :)
p.s. This example doesn't win a 'useless use of cat award' ;) http://porkmail.org/era/unix/award.html