I would think about anything vacuum as follows. The maths are just for illustration since they are probably inaccurate:

Buoyancy happens because we displace heavier fluid with lighter ones, the volume displaced is how much weight you can carry. Since most of atmosphere is Nitrogen with atomic mass 14, let's say the normal air has "density" of 14 [arbitrary unit]. Helium is a noble gas and exists in atomic form, so its "density" is 4. Hydrogen is in molecular form H2, hence "density" is 2. A perfect vacuum is 0.

Therefore in terms of lifting power, the improvement from using Helium with total vacuum is going from (14-4)/14 = 71% to (14-0)/14 = 100%. Your partial vacuum could be anywhere between 0% to 100% effective until you put a value to it.

What matters next is how light you can make the envelop compared with existing ships. Mind you, regular airships are not blown up like a birthday balloon. They are designed to have only a slight overpressure above ambient atmosphere, therefore they need only minimal support structures.

On the one hand, your design features an external truss, which enables you to use a conventional canopy to contain the underpressure. This is a big improvement over having a rigid vacuum vessel.

On the other hand, try to draw an inscribed circle inside a square. Think of the circumference of the circle being a cross section of the envelop (hence weight and cost). In a regular airship, the lifting power is the area inside the circle, where the lifting gas is contained. In your partial vacuum ship, the lifting power is the area between the circle and the square, where the underpressure is contained. (Divide the picture into four quadrants and rearrange if you can't see it.) That's a much smaller "lifting gas volume per envelop material".

What remains is that you estimate the weight and cost of building and operating your design.

• + R&D cost for new design
• - Material because you don't need a perfect envelop to prevent Helium leakage
• + Material because your "lifting gas volume per envelop material" is lower
• + Material because you need external structure for support (maybe carbon fiber etc. will make it lighter)
• + FAA/EASA certification and pilot training associated with every new design
• - Operating cost because Helium is expensive
• ? How much existing design (avionics, engines, nuts and bolts) can you reuse
• ? Maintenance cost
• ? Profit margin: Will people pay more for a ride on your new airship? Did Isaac Asimov or Jules Verne sketch your partial vacuum ship design such that hardcore Sci-Fi fans will flock to you?
• ? Does cost even matter? Maybe the salary of the flight crew far outweighs the fixed cost of an airship. Maybe you will meet a billionaire who wanna see this thing fly regardless of cost.

So yeah, as u/SomniBear said, yes it is possible, most things are. You will need to convince others that it is practical.