Vapour-cell spectroscopy is widely used for the frequency stabilisation of diode lasers relative to specific atomic transitions -a technique essential in cold atom and ion trapping experiments. Two laser beams, tuned to different frequencies, can be overlapped on the same spatial path as an aid to compactness; this method also enhances the resulting spectroscopic signal via optical pumping effects, yielding an increase in the sensitivity of spectroscopically-generated laser stabilisation signals. Doppler-free locking features become visible over a frequency range several hundred MHz wider than for standard saturated absorption spectroscopy. Herein we present the measured Doppler-free spectroscopy signals from an atomic vapour cell as a function of both laser frequencies, showing experimental data that covers the full, 2D parameter space associated with dual-frequency spectroscopy. We consider how dual-frequency spectroscopy could be used for enhanced frequency-stabilisation of one laser, or alternatively to frequency-stabilise two lasers simultaneously, and analyse the likely performance of such stabilisation methods based on our experimental results. We discuss the underlying physical mechanism of the technique and show that a simple rate-equation model successfully predicts the key qualitative features of our results.