Your daughter might even be (likely) totally aware on how to handle this properly.
To me, this sounds like a problem that's not so much an issue of practical nature, as it appears to be a matter of trust, empathy and mutual respect. You guys need to put understanding of each others perspective in front of anything else.
Even though it's just words, and your husband might have expressed it differently, I think it sounds "funny" to me when you state that he says he doesn't tolerate her. There's a distinct difference between that, and not tolerating the outcome of things she does (i.e. not her in person). Perhaps it's your husband and your daughter that needs to talk, in a different way and communicate better? It really appears that you've done more than your fair share in this regard – what about him?
How about asking him to try and be more gentle. Seriously. (Being gentle does not mean you're selling out on the integrity of your concerns, by the way.)
He only needs to put it somwhere along the lines of …
"Hey sweetie. (Looking her in the eyes.) You know... This doesn't really work, right? Have you and mom talked this over, how to handle these pads? You see (look her in the eyes again if needed), dad's a little sensitive to blood. Don't you agree this is better placed in the dust bin anyway?".
… Being on HER side is the ONLY path out of this and similar situations. Get used to it: It may seem like the wrong thing to do – like handing over all the keys to HER and loosing your own will and power to command – but really, that's what needs to be done. Eventually, she'll be the sole commander of her own actions anyway. And maybe that's just what she needs, to be confirmed by you guys. Try to act more supportive in this matter, and don't alienate her in this – for her – new situation beginning to have her period. Sometimes her personal insights will come slowly, sometimes fast. Like you and me, right? Personal development isn't a fixed rate curve. Again, it's ALLRIGHT to progress slowly, as much as it is to do it quickly, in this regard. Only nature decides what's the proper/unique progression for your daughter. You guys are only there to support THAT curve. HER progression/development. NOT to support your own ideals of comfort, EVEN though I (as a parent to three 2/4/7 year old manic troll sons) have your full compassion and sympathy for the constant lack of energy a parent might suffer from. It comes with the territory, so to speak, from the day you choose to be a parent.
As further advice, I think you should be prepared for the possibility that you might have to rinse and repeat this procedure a few times. (Bonus: for increased effect, try taking it from different angles each time, while keep telling it like a friend; provide nuances that might help support her personal insight.) All in all, if multiple times telling this is what it takes, refrain from freaking out, say, the third time … You're about to establish something that may or may not be new in her relation to her parents: trust. Real trust. Trust, as in friendship. And friendship as in, people who are looking up to each others greatness. It's delicate. But please don't ruin that bond – it's your foundation as a family – or the problems might start to multiply themselves if you establish trust, then break it.
Good luck and all well to your whole family, Tiffany!