Down to ~hold hands~. To the Mormon Church, this is just as bad as being dtf.
DAWG I AM SOOO DTHH WITH THE CHICK WHO IS ONLY MODERATELY ATTRACTIVE YET HAS A GOOD PERSONALITY
Down To Hold Hands. A derivative of DTF, except instead of the person being down to fuck, which usually implies that they are not looking for a long-term relationship, DTHH implies that the person is.
Andy: That girl looks like she's DTHH.
Steve: She definitely looks like relationship material to me, you should go for it.