As of WP-Members 3.1.0, multiple selection checkbox support is an included feature in the plugin. That makes custom implementation such as described here unnecessary for most applications. I am leaving this post here however as there may continue to be users who (1) need a high level of customization that may utilize some or all of this kind of approach, and (2) for users who may not update to 3.1+ who need this support.
Note that there is now a more flexible example of multiple selection checkboxes here. This example is easier to set up and allows for multiple checkbox groups.
Something that will probably become a full feature in the main plugin is multiple selection checkboxes. However, until that becomes a full feature, here is a code snippet that you can use to set this up in your existing installation.