The haptic sense relies upon a plurality of receptors and pathways to produce a complex perceptual experience of contact, pressure, taps, vibrations and flutters. This complexity is yet to be reproduced in haptic feedback interfaces that are used by people controlling a dexterous robotic hand, be it for limb-absence or teleoperation. The goal of the present bimodal haptic armband is to convey both low-frequency pressure changes and high-frequency vibrations from a dexterous robotic hand to a human's upper arm, so as to guide his/her control of the artificial limb. To that end, we design and manufacture four novel soft robotic armbands combining inflatable air chambers and vibrotactile stimulators. We develop control systems for both pathways. We conduct a series of benchtop tests to determine the pneumatic and vibrotactile performance and select from competing designs and materials. We test two of the resulting bimodal haptic armband on human subjects and confirm their ability to use both aspects of this haptic information. Arguing that dexterous artificial hands are presently not used to their fullest capability by the dearth of haptic information in users, this work aims to achieve a more realistic tactile experience for a fluent, more natural usage of robotic artificial hands.