It is possible to support both block and character access to a device: block access to support filesystem operations, and character access in order to allow a user process (typically one started by a system administrator) to read, write, or control the device directly.
For example, the Silicon Graphics disk device drivers support both block and character access to disk devices. This is why you can find every disk device represented as a block device in the /dev/dsk directory and again as a character device in /dev/rdsk ("r" for "raw," meaning character devices).