Do you have a "bug out" plan for your significant other? What are they going to take to support themselves while they are gone? What's the plan of action? Some have tornados, other have hurricanes, and yet others experience blizzards. Know your environment, and go over plans. Train and plan for your family. Often, telephone and some cell lines can be overcome or systems become compromised. Have a signal of safe arrival; this call may only last a second. Try texting, for it goes over a different line altogether and may work when others do not. Have a secondary method to charge your cell phone, auto, or external battery pack.
Do you have adequate supplies at the residence to make it through several days of no shopping or electricity? I always suggest canned foods or even MREs (Meals Ready to Eat), bottled water, and energy bars. As I was told in the Army, "It's not what you eat, but rather that you eat."
Do you have cash? ATMs go down in bad weather and a good run could deplete them. How about a "bug out" bag for the family? If you only had time to grab the family and one thing, this is it.
One thing I'm big on are these big plastic tubs with locking lids; you can find them at most any home improvement store. These are the ultimate family bug-out invention. Get a few that will fit in the back of the family vehicle. During weather seasons where bugging out is a possibility, have them pre-packed in advance. Pack one with "needful things." Have a second tub for extra clothes and comfort items; remember, this is a two-minute warning drill here. These are to be grabbed and gone with the family. There's no time for packing.
I know you thought that when you came on the job that you would be cared for by the department. Yes, but not solely. Some departments have plans and shelters for families of first responders. What I recommend is a family drill. Have them prepare to evacuate in two hours or less; this is an adequate warning for some accidental events.