Cheaters lie. Period. Cheaters will do anything they can do to deflect their transgressions and make you the crazy one. Period.
Your H is not unique. No cheaters are.
If your H (or any spouse for that matter) was or currently is in an affair they lie and deflect.
If you placed a pile of gasoline soaked newspaper in your living room along with a bunch of tree branches would you be shocked when it went up in flames from the smallest spark? Probably not. On that note, don't be shocked your H is lying and deflecting.
Your H might be removed from OW due to the job situation but that doesn't necessarily mean he is removed from her totally. Affairs are powerful and lingering. Especially when they have a second option available to them. What should be urgent (dumping OW and putting all focus on the M) is not with a wayward spouse.
For months and months I got tied up with talks with my H that would go on for hours. It was abusive and I never should have participated. It was simply a way for him to purge his guilt yet keep on truckin' down the affair and divorce path. Don't put yourself in the same position I did unless you are certain it is only you and your H in the talks.