In most states, a spouse cannot be “cut out” of a Last Will and Testament, even if it is a “new spouse” and an “old will”.
Even if a spouse is not named specifically in a Will, that spouse will be able to “elect against” the Will and would be entitled to 40% to 60% of the estate through the courts, depending upon what state that the decedent resides.
However, in order for your husband (and you, his children and his estate) to avoid the considerable cost and effort required to “elect against” a Will, it may be far more appropriate to create a new Last Will and Testament naming the spouse as a beneficiary in the Will (as a court would do the same should it come to that).
Standard Legal offers a do-it-yourself Last Will and Testament legal forms software package that is under $15 and is very simple to use to create a new Will that reflects the current marriage.