// Your moment
var mmt = moment();
// Your moment at midnight
var mmtMidnight = mmt.clone().startOf('day');
// Difference in minutes
var diffMinutes = mmt.diff(mmtMidnight, 'minutes');
By default, moment#diff will return number rounded down. If you want the floating point number, pass true as the third argument. Before 2.0.0, moment#diff returned rounded number, not a rounded down number.
Consider this pseudocode because I haven’t test to see if the difference takes into account DST.