We propose to study the combination of acoustically transparent tangible objects (ATTs) and ultrasound mid-air haptic (UMH) feedback to support haptic interactions with digital content. Both these haptic feedback methods have the advantage of leaving users unencumbered, and present uniquely complementary strengths and weaknesses. In this paper, we provide an overview of the design space for haptic interactions covered by this combination, as well as requirements for their technical implementation. Indeed, when imagining the concurrent manipulation of physical objects and delivery of mid-air haptic stimuli, reflection and absorption of sound by the tangibles may impede delivery of the UMH stimuli. To demonstrate the viability of our approach, we study the combination of single ATT surfaces, i.e. the basic building blocks for any tangible object, and UMH stimuli. We investigate attenuation of a focal point focused through various plates of acoustically transparent materials, and run three human subject experiments investigating the impact of acoustically transparent materials on detection thresholds, discrimination of motion, and localization of ultrasound haptic stimuli. Results show that tangible surfaces which do not significantly attenuate ultrasound can be fabricated with relative ease. The perception studies confirm that ATT surfaces do not impede perception of UMH stimulus properties, and thus that both may viably be combined in haptics applications.