Yes you can schedule whole families in a single position by turning on the "Never split up family members in this ministry" option for the ministry of the position. This feature is often used to schedule, for example, one family per service in the Greeter ministry as opposed to always scheduling a fixed number of ministers.
1. First, select the appropriate ministry in the Ministries pane and clicking the Edit Ministry button.
2. Check the "Never split up family members in this ministry" box and then click OK.
3. Then, in the Service Times pane you will want to require just one (1) volunteer for each service.
Even though you only require one volunteer, MSP will automatically overload the position with all volunteers that are qualified for the position in one family.