Is it possible to play sound through both the headphone jack and my internal speakers?
In my experience, the answer is no. As soon as you plug in the headphones into the 3.5mm jack, it replaces the internal speakers as the default output (and vice versa when you unplug them). There are several discussions around as to whether this is actually a limitation in the hardware or the software, but the end result always seems to be the same. 

Now this may not answer specifically what you're asking, but for interest, the only time I've had any success with simultaneous headphone and speaker output is when using a USB device, such as a headset or USB speakers. In order to get this to work, you'll need to plug in the USB device, then do the following:


Start the Apple "Audio MIDI Setup" utility (/Applications/Utilities/Audio MIDI Setup) 
Select the "+" in the bottom-left and select "Create Multi-Output Device"


Select the Multi-Output Device that has been added and in the right-hand pane, select both the "Built-in Output" and your USB device. That should look something like this:


Start "System Preferences" → "Sound" and click the "Output" tab. Select the "Multi-Output Device" that's now there.


An unfortunate side-effect of this, as "The selected device has no output controls" eludes to, is that you now can't control the volume in the normal manner. To do this, you'll have to go back to Audio MIDI Setup and do it from there for each of the outputs. So be careful with those headset and speaker levels to begin with!!!




And that's it :) So, now when you play a song in iTunes, for instance, that should come out of both the headset and the speakers.

However, whilst all this may be largely academic without a USB headset or speakers, I did also come across the Griffin iMic which says:


  iMic supports both mic and line level inputs via a selectable switch,
  and provides a line-level output for connecting speakers or
  headphones.




I've not tried it, but if you're willing to spend the money, that may allow you to connect a pair of headphones with a normal 3.5mm jack then, using the method above, get audio out of both the internal speakers and the headphones simultaneously.