There's no secret about it: the Phillies suck at interleague play. Since 1997, when interleague play started, their record against the AL is 93-118 for a .441 winning percentage. (Of course, that's during the regular season. In the post-season, their record is 4-1.) Going into this season, only 3 NL teams had worse interleague play records than the Phillies.
One theory that always gets bandied about with respect to interleague play is that the NL has a distinct disadvantage because NL teams don't have a DH. The AL teams spend big money on filling a roster spot with a hitter whose job is specifically to hit and not field. The NL teams, playing in a leauge without a DH, don't fill a roster spot with that job in mind. Thus, when they have to play AL teams in AL parks during interleague play, they have to fill the DH spot in the batting order with their best bench guy (or put a regular in the DH spot while plugging that regular's position with a bench guy, which has the same effect).
In theory, this seems like a very reasonable explanation for the fact that the AL has dominated the the NL in interleague play. From 1997 through the start of this year, the AL has won 1536 interleague games while the NL has won 1420 for a .520 AL winning percentage.
However, the fact of the matter is that the DH rule is decidedly not the reason the Phillies are horrible in interleague play. How do we know this? The Phillies are better on the road during interleague play. Here's a simple chart showing the Phillies home/road splits for interleague play since 1997 (and including this year):
So, on the road where they have to use the DH, the Phillies are slightly better than at home, where the AL team can't use its DH.
Thus, whatever is the cause of the Phillies' ineptitude during interleague play, it's not the DH.