I can't tell you how but FWIW when I set up Family Room, there was a Microsoft article explaining how to share the calendar with iPhone and Android users. Fortunately there were only WPs in the family so I didn't pay a lot of attention to it.
Both of you have to have a Microsoft account. Share a calendar and add the outlook account on the iphone and it should be one of the calendars which can be displayed on the iphone calendar.