As other's have mentioned in some jurisdictions this type of product is called second to die insurance. Alternatively it is called a Joint Life Second Death (JLSD) policy.
The premium for such a product will typically be smaller than a Single Life policy or a Joint Life First Death (JLFD) policy of the same duration, but it depends on how your insurance company structures the premium.
Typically these types of polices are taken out as Whole of Life (WoL or WL) policies (at least where I am located UL (Universal Life) is not a product sold on the market). Whether or not a term or WoL product is more appropriate for you is something you would need to consider.
You may also want to take out accident insurance or Permanent Disability Insurance (TPD) to mitigate against the situation where one of you survives but can't provide for your children.
You can also take out a policy that pays out twice, once for each life. These types of policy are called Dual Life (typically). They should (in general) be equivalent to a JLFD policy and a JLSD policy added together (though two separate policies may be slightly higher due to having to account for setting up two policies instead of one).
It is also possible to get deferred versions of these polices, which defer the start date of the policy to some point in the future.
Finally, you can get Unit Linked (investment style policies) and With Profits (aggregated investment type policies) which can augment the payout (but carry some investment risk as well).
As with anything potentially this complicated it is worth getting professional financial advice on.