Under Georgia v. Randolph, 547 U.S. 103 (2006) in such a case the police may not lawfully enter without a warrant, and if they do enter, any evidence found will not be admissible.
The court in Georgia v. Randolph said:
[N]othing in social custom or its reflection in private law argues for placing a higher value on delving into private premises to search for evidence in the face of disputed consent, than on requiring clear justification before the government searches private living quarters over a resident’s objection. We therefore hold that a warrantless search of a shared dwelling for evidence over the express refusal of consent by a physically present resident cannot be justified as reasonable as to him on the basis of consent given to the police by another resident.
However, the police may talk to either or both occupants at the door, and this may provide sufficient reason to obtain a warrant. If police determine that someone in the residence is in danger, they can enter on that basis, and anything in plain view may be treated as evidence.
Further consider Fernandez v. California, 571 U.S. ___ (2014) In that case one occupant of an apartment denied consent for police to enter. But the police had probable cause to arrest him, and did so. An hour later police returned and got consent from the other occupant, who may also have been a victim of domestic assault by the first occupant. The consent search was upheld, as the objector was no longer present (being then detained) when the police asked to search. So the holding about divided consent applies ONLY if the objector is physically present. If only one occupant is present, that occupant may consent to a search, even if the police know very well that the other lawful occupant would have objected. Interestingly, in Fernandez it appears that police had ample probable cause and could easily have secured a warrant, but chose to proceed on the basis of consent instead.