Jason,
I think you are encountering a current limitation. But you should still be able to draw the layer with its multi-layered symbol...
If you want to draw multi layered line symbols, then you need to access the map service. I tested this out with my own server by publishing a line layer that uses a 3 layered line symbol in ArcMap for "expressway" and it drew correctly in the ArcGIS Online map viewer. On the service, I configured it for the "best" anti-aliasing.
If you access the feature service or an individual layer of a map service via it's index, complex multi-layered symbology is not supported. This is because how the layer gets drawn. With map services, the layer is drawn by the server and returns an image to the client. The server draws the complex line symbol in much the same way ArcMap would. When you access a feature service or individual layer of a map service, the server returns the x,y coordinates of all features and relies on the client (web browser, mobile device) to draw it. These features get drawn as graphics on the client and the clients have pretty limited drawing abilities. This is why you only get a simple line symbol.
We are looking at ways to improve our client side drawing (SVG, Canvas), but this is a work in progress. So in the mean time, you'll have to rely on the map service to draw such symbols.
Thanks,
Mike