My common law husband died in feb. he left me the house if I survive him by six months. Then the house becomes mine. Who is responsible for the mortgage in the six month waiting period me or his estate

Was this information on the 6 month waiting period part of a will? Does the will give further instructions ?

No common law in ND.
North Dakota Common Law Marriage - Labor Law Talk Blog (http://blog.laborlawtalk.com/2006/11/10/north-dakota-common-law-marriage/)
One way or the other you better keep the mortgage current. Otherwise you may lose it under foreclosure. Read his will, what does it say? Who is the executor?

A WILL comes first.
The LAWS of North Dakota come second.
Without a will and without benefit of marriage, you could lose the house to his blood relatives under 'intestate' laws.

If there is a will, the will needs to be probated, during which time any bank accounts he has are used by the bank to pay bills, including the mortgage.
You (or anyone) can apply to the probate court to be executor.
Between the funeral director and the bank, all these questions can be answered.

I assume there must be a will, given the 6-moth time period requirement. Until the house becomes yours the estate is responsible for paying ongoing expenses of the estate's assets, such as the mortgage and taxes on the house. But as others have noted, in the mean time it's definitely in your best interest to make sure that the executor of the estate is keeping up with these payments.

No common law in ND. ...

Apparently not (No common law marriage). But it's probably neither here nor there, assuming that OP was left the property by will.