The rising density of wireless devices, combined with the availability of a plethora of wireless web applications, has overcrowded the radio frequency spectrum. Majority of the present wireless radio spectrum is already licensed; however, studies have shown that the licensed spectrum is significantly underutilized. Cognitive Radio Networks (CRNs) are envisioned to utilize the radio spectrum more efficiently. CRNs may be required to handle both unicast and broadcast traffic, which makes the task of channel assignment in CRNs more challenging, as communication mode required for each type of traffic is different. Unicast traffic may suffer due to interference if the same channel is assigned to and used by neighboring nodes; on the other hand for broadcast traffic if a larger set of neighbors share a common channel, any particular node may exploit wireless broadcast advantage to communicate with a maximum number of neighbors in a single transmission. Existing channel assignment schemes either favor unicast or broadcast traffic only. In this paper a Unified Channel Assignment (UCA) algorithm is proposed which assigns channels according to their respective interference and connectivity parameters depending on the proportions of unicast and broadcast traffic in the network.