While there is no specific weight generated for families, The Census Bureau uses Housing Unit Weights to generate family-level estimates. A little bit more info on the matter can be found in this forum response. Using the household weight you should be able to get close to published estimates, however, the Public Use file is a subset of the full sample and is subject to additional sampling error and further processing before being released so it is not likely that you will get the exact same figure.
I hope this helps.