Thomas Myers / Retna Digital 1 / 6
Thomas Myers / Retna Digital 1 / 6

Nothing much shocks us about Charlie Sheen anymore, other than the obscene amount of money he earns per episode of "Two and a Half Men." But even we were a bit taken aback by the latest cover of In Touch.

No, not because of the headline that screams, "Charlie caught cheating." Or the teaser that claims he promised wife Brooke Mueller he's "a changed man" but has been "sneaking out of rehab for a sordid affair with a lingerie model."

None of that, if true, is surprising. What amazes us is that he allegedly did this while wearing a fake mustache that appears to have been hatched from an unholy union between Ned Flanders' fuzzy soup strainer and the exaggerated lip tickler sported by Mario in "Donkey Kong."

RELATED: See more pics, sans mustache, of Charlie

It's all part of what the tabloid dubs "the dumbest disguise ever," which comes complete with hoodie and sunglasses.

The embattled star, who is facing domestic violence charges following a Christmas Day dustup with Mueller in Aspen, Colo., supposedly engaged in this not quite James Bond-level of stealthiness on April 7 to avoid the paparazzi while visiting the home of one Angelina Tracy, the aforementioned model (and alleged part-time, ahem, professional companion).

"He ran down to his car," recalls an eyewitness. "It seemed like he wanted to leave as quickly as possible."

RELATED: Is Charlie leaving "Two and a Half Men"?

According to the magazine, Sheen, who is seeking treatment at a Malibu rehab facility, has been "regularly" seeing Angelina, who, for all we know, could simply be modeling unmentionables he plans to buy for Mueller (now that would be truly shocking), the rehab-receiving mother of his 1-year-old twin sons, Max and Bob.

"He is seeing Brooke and the kids a lot and is good about continuing treatment," relays an insider. "He has been sweet to Brooke, and promises her that he's changed."

Speaking of being sweet, the tab maintains that Charlie recently picked Angelina up in a chauffeur-driven Mercedes and surprised her with flowers and other gifts. What a thoughtful guy. Less thoughtful: Accusations that he brought Tracy back to his mansion.

Anyhoo, Sheen's reps did not respond to our request for comment on the bushy mustache-garnished assertions, although an explanation was offered to E! News.

"The woman in question is the sister of one of Sheen's campmates, and Sheen was only responding to a 12th-step call," states his spokesman. "Since Sheen knew he was being followed and how this would look, he wore the mustache in a tongue-in-cheek disguise gesture."

RELATED: Hollywood's cheated hearts club

It's shaping up to be a busy week for the actor's people. TMZ reports that his attorneys have moved to suppress "incriminating statements" he made to police during the holiday altercation with Mueller, during which he allegedly threatened her and held a knife to her throat.

The argument: Sheen wasn't read his rights, although you'd think he'd know 'em by heart at this point.

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