No, they're not merge-mineable and you'll have to pick from one or the other to mine. Just because both ETH and ETC use the same algorithm to mine doesn't mean they're merge-mineable, and if you're looking for coins to merge-mine with ETH,
Claymore's dual miner offers some options, though keep in mind many of the merge mineable coins like Sia have been dominated by ASICs and thus aren't too profitable anymore- it is better to just plain mine ETH or ETC at the moment to keep electrical costs down.