CDMA has two different channels. One is for voice, 1xRTT. One is for data, EvDO. While the technology technically could support using both at the same time, the standard does not. Verizon implements the standard as it was written. Recently the CDMA Development Group published an optional CDMA specification that will allow both to be used. I don't think anyone implemented it yet, and the probably won't with LTE right around the corner.
AT&T uses a different standard where voice and data is sent over the same pipe. They do not separate voice and data over different channels, and yet it still allows voice and data signals to be sent at the same time.