RF 433 Module with VirtualWire: transmit and receive using the same Arduino board
These lines in the ISR in VirtualWire.cpp

    if (vw_rx_enabled &amp;&amp; !vw_tx_enabled)
        vw_rx_sample = vw_digitalRead_rx() ^ vw_rx_inverted;


and

    if (vw_rx_enabled &amp;&amp; !vw_tx_enabled)
        vw_pll();


mean that the receive path code is just not executed while the transmitter is enabled.

It kind of seems from the comment as that might not have been true at some point in the past, though I'm not seeing a version history for an "official" version to check.  

You could try to modify the code to implement both, but it is worth noting that VirtualWire has been deprecated in favor of the more versatile RadioHead, so you might want to evaluate that and perhaps make modifications there instead.