This plugin provides a field type that looks exactly like Craft's default Checkboxes field, but stores a boolean value to the database (similar to the Lightswitch field), so you can use a custom field parameter in your ElementCriteriaModel.
To install the plugin, copy the checkboxfield/ folder into craft/plugins/. Then go to Settings → Plugins and click the "Install" button next to "Checkbox Field".
Custom field parameter usage:
{% set entries = craft.entries.myCheckbox(1).myOtherCheckbox(0) %}
Uncheck "Show field name and instructions" to hide the field's name and it's instructions. This also removes the top margin, to make multiple Checkbox fields look like Craft's default Checkboxes field with multiple options.