Your husband has admitted to having an emotional affair but denies a physical affair , yet the other woman (she is the other woman, not a friend, not a workmate, they are at the very least having an emotional affair) sends him photos of her underwear late at night.
I have many good male friends, I have never sent any of them teasing photos of my underwear.
He has been both texting her (noted from the phone bill) and presumably deleting them? have you seen the texts?
He has also been whattsapping her which is what you have already found, these will not show up on phone bill so probably his contact is much higher than you have knowledge of.
Innocent people do not delete texts. Regardless of what was in the texts, your husband and this woman have a secret relationship that you are not involved in.
From what you have said, you have been having a pretty rough time recently, your husband has manipulated this into poor him wanting to be some sort of hero and not bother you but instead spend hours talking to another woman instead, please please see what he has done there, its called gaslighting, its making you doubt yourself and think he is actually doing nothing wrong, its making him the victim and you the bad guy.
Like others say, when people are caught out having an affair (both emotional and physical) they generally follow the same pattern, they will minimise, play it down, lie about how far it has gone, they will gasllight, make you feel like you are the unreasonable one.
Your husband had a choice whether to be supportive to you when you were going through a bad time or to instead develop a secret relationship with this woman.
Im so sorry you are having to go through this is there any way you can take some time off work and go away with the children to clear your head? Or tell him to leave while you decide what you want to do.