Try adding
data-mini="true"
to the select box. It will display the minified version of the select box. Also you cannot have exact height match for both the input types you would need to modify the css as well.
Try this jsfiddle. http://jsfiddle.net/Bp2eX/2/
I also was trying to use the custom jquery mobile plugin. just use in place of the date field. Do try it.