Using an IR diode as an emitter and receiver?
Basically, a LED is just a diode. 

If you take a diode and bias it in reverse, no current flows through, because there's no hole/electron recombination happening.

Now, that "no" is a bit of a stretch: of course, due to thermal effects, pure luck (tunneling), a few electrons and holes will still recombine. 

Now, in an LED, a photon hitting the carrier-depleted zone can actually create a hole-electron pair and thus lead to a elemental current flowing, if there's not an instant recombination happening within the junction. The likelihood of the electron actually being "drawn" out of the semiconductor junction grows with the strength of the electrical field it's subject to – in other words, on the voltage across the diode.

Do that with enough photons, and your diode in reverse bias suddenly starts conducting a bit of current!

However, that current is not going to be very large. And the percentage of electrons and holes spontaneously recombining still will be pretty high. To make this work, you'll need to bias your LED with a "high-ish" reverse voltage – don't overdo it, LEDs will be damaged if you exceed the reverse voltage rating. 

But if you reverse bias a diode, and then either measure the current through it (e.g. with a Darlington array) or for example the time it takes to discharge a small capacitor, then you can make a light sensor.

Problem: That current is going to be small.

Problem2: a diode in reverse bias is a capacitor of its own, which severely limits the speed at which you can receive bits.

Problem3: switching between transmit and receive mode requires a lot of protocol logic.

However, this can still work. Start slow; you will most definitely be able to measure a different current in dark and light conditions. (been there, done that with very red LEDs, and a reverse bias close to their maximum rating).

Getting data at reasonable rates (> 5 bd) across will be a bit challenging if you really expect "on/off" to work.

I'd be tempted to say that a low-count amplitude shift modulation on the TX LED current, quite possibly with some predistortion applied to counter the whole nonlinearity, would give you reasonable data rates, something in the single digit kilobaud, possibly! You'd need to build a bit of a nice, low-noise current amplifier, however.