You can use Date.getTime() which:
Returns the number of milliseconds since January 1, 1970, 00:00:00 GMT
represented by this Date object.
This means you can compare them just like numbers:
if (date1.getTime() <= date.getTime() && date.getTime() <= date2.getTime()) {
/*
* date is between date1 and date2 (both inclusive)
*/
}
/*
* when date1 = 2015-01-01 and date2 = 2015-01-10 then
* returns true for:
* 2015-01-01
* 2015-01-01 00:00:01
* 2015-01-02
* 2015-01-10
* returns false for:
* 2014-12-31 23:59:59
* 2015-01-10 00:00:01
*
* if one or both dates are exclusive then change <= to <
*/