Have a look at the system Berg toys use for their go-karts. Its called a BFR hub (for brake, forward and reverse). This hub lets you go forward or backward, while always pedalling in forward direction. It also has a freewheel.
The system needs two chains, with this being in the middle of your drive sprocket and axle sprocket.
Hub: BFR Hub stands for brake, forward and reverse; this hub allows the rider to pedal forward, coast with the pedals remaining static, pedal back slightly to engage the coaster brake or use the hand brake to stop, once stopped pedal backwards to go in reverse!
Source: Product page for Berg John Deere BFR go-kart
Of course, it is not sold (or even meant) for bicycles, so you'd need to either adapt it for a bicycle, or build your own. However, it shows how much technical effort is necessary to combine reverse gear and freewheel.