I used to be able to get it like this:
directionsService.route(directionsRequest, function(directionsResult, directionsStatus) {
var directionsRenderer =
Take a look here:
The Directions Results Object
It looks like you now have to sum up each leg distance.
legs[] contains an array of DirectionsLeg objects, each of which contains information about a leg of the route, from two locations within the given route. A separate leg will be present for each waypoint or destination specified. (A route with no waypoints will contain exactly one DirectionsLeg.) Each leg consists of a series of DirectionSteps.