Herein, we demonstrate the first fabrication of stacked-layer heterostructure films (denoted as TP/EG) from thiophene (TP) nanosheets and electrochemically exfoliated graphene (EG) for high-rate and flexible ASSSs (TP/EG-ASSSs) and micro-supercapacitors (TP/EG-MSCs) with superior rate capability and enhanced volumetric capacitance. The heterostructure films with a thickness of ~105 nm are produced by alternating deposition of electrochemically EG nanosheets (≤3 layers) and redox-active conducting TP nanosheets (thickness of 3.5 nm) in sequence, and exhibit large-area uniformity. Notably, the produced films were directly transferred on a polyethylene terephthalate (PET) substrate and served as binder- and additive-free electrodes for flexible supercapacitors. Remarkably, the resulting TP/EG-ASSSs exhibited a pronounced pseudocapacitance contribution with strong redox peaks, and delivered an areal capacitance of ~3.9 mF cm-2 and a volumetric capacitance of ~375 F cm-3, energy density of 13 mWh cm-3 and power density of 776 W cm-3. Meanwhile, the TP/EG-MSCs can be operated at high rate of up to 1000 V s-1, offering ultrahigh rate capability, e.g., with a landmark areal capacitance of 1.30 mF cm-2 and volumetric capacitance of 123 F cm-3 at 100 V s-1, as well as unprecedented flexibility under different bending states.