At some point Abaroth has published all symmetric shapes with six unit holes that can be formed with the Tetrahexes. There are 31 of them (one for each day of the month). I recommend visiting the site: each shapes is shown in grey but when you pass the mouse pointer over it, a solution appears.
A natural question would be: how many of these 31 shapes are bi-tilable, i.e. can be tiled with the Heptiamonds? The answer is 8. Unlike Abaroth, I show each shape directly with a solution; these are accompanied by the following information: reference number from Abaroth's page, perimeter, degree of symmetry and total number of heptiamond and tetrahex tilings. There is a total of 100 different heptiamond tilings for all 8 shapes together; the tetrahex tilings are 17.
All of these have axial symmetry -- none of Abaroth's 9 shapes with central symmetries is bi-tilable. While Abaroth's shapes have a perimeter in the range [78, 90], only for the smallest values do we obtain a Heptimond tiling. This is because of the limited hexagonal congruency of the set. Notice also the great disparity in the counts of distinct tilings: two shapes have a unique solution, most are under 10 and just one reaches 70 solutions.
One of these, Abaroth's n° 3, has a ternary symmetry and can also be found on George Sicherman's site.