The opportunity for online engagement increases possible exposure to potentially risky behaviors for teens, which may have significant negative consequences. Effective family communication about online safety can help reduce the risky adolescent behavior and limit the consequences after it occurs. Our paper contributes a theory of communication factors that positively influence teen and parent perception of communication about online safety and provides design implications based on those findings. While previous work identified gaps in family communication regarding online safety, our study quantitatively identified the factors that significantly contribute to parents' and teens' differing perceptions. We analyzed data from a survey of 215 teen-parent pairs through a cross-sectional design and examined the factors that contribute to increased family communication about online safety. For parents, active mediation, technical monitoring, and a perceived positive affect of the teen were associated with higher levels of family communication. Our results were similar for teens, except that the teen's online safety concern and parental monitoring were also positively associated with increased family communication, while restrictive mediation was associated with lower levels of family communication. Many existing designs for online safety support a restrictive approach, despite teens not wanting technical restrictions. A key implication of our findings is that teens view active mediation and monitoring positively in respect to family communication. Contrary to mainstream narratives, this finding suggests that teens value parental involvement and do not desire complete independence online. By examining specific mechanisms which can hinder or improve family communication between parents and teens regarding online safety, we recommend solutions that give teens an active role in their online safety and facilitate effective family communication through cooperation between both parties, rather than technologies that promote parental restriction.