Tested the game myself and for me, the character models are not visible. Only clothing and weapons, floating around in the air. Proton 3.7.3 or 3.7.5 beta makes no difference for me.
Someone else had the same problem:
https://spcr.netlify.com/search?q=mordheim

My specs:

Computer Information:
Manufacturer: Unknown
Model: Unknown
Form Factor: Laptop
No Touch Input Detected

Processor Information:
CPU Vendor: GenuineIntel
CPU Brand: Intel(R) Core(TM) i7-6700HQ CPU @ 2.60GHz
CPU Family: 0x6
CPU Model: 0x5e
CPU Stepping: 0x3
CPU Type: 0x0
Speed: 3500 Mhz
8 logical processors
4 physical processors
HyperThreading: Supported
FCMOV: Supported
SSE2: Supported
SSE3: Supported
SSSE3: Supported
SSE4a: Unsupported
SSE41: Supported
SSE42: Supported
AES: Supported
AVX: Supported
CMPXCHG16B: Supported
LAHF/SAHF: Supported
PrefetchW: Unsupported

Operating System Version:
Ubuntu 18.04.1 LTS (64 bit)
Kernel Name: Linux
Kernel Version: 4.15.0-33-generic
X Server Vendor: The X.Org Foundation
X Server Release: 11906000
X Window Manager: GNOME Shell
Steam Runtime Version: steam-runtime-beta-release_2018-06-14

Video Card:
Driver: NVIDIA Corporation GeForce GTX 1060/PCIe/SSE2
Driver Version: 4.6.0 NVIDIA 396.54
OpenGL Version: 4.6
Desktop Color Depth: 24 bits per pixel
Monitor Refresh Rate: 60 Hz
VendorID: 0x10de
DeviceID: 0x1c20
Revision Not Detected
Number of Monitors: 1
Number of Logical Video Cards: 2
Primary Display Resolution: 1920 x 1080
Desktop Resolution: 1920 x 1080
Primary Display Size: 13.54" x 7.64" (15.51" diag)
34.4cm x 19.4cm (39.4cm diag)
Primary Bus: PCI Express 16x
Primary VRAM: 6144 MB
Supported MSAA Modes: 2x 4x 8x 16x

Sound card:
Audio device: Realtek Generic

Memory:
RAM: 15915 Mb

Miscellaneous:
UI Language: English
LANG: en_US.UTF-8
Total Hard Disk Space Available: 516306 Mb
Largest Free Hard Disk Block: 387176 Mb
VR Headset: None detected

Recent Failure Reports:

Someone suggested a workaround here for standard Wine, setting a registry value:
https://appdb.winehq.org/objectManager.php?sClass=version&iId=33164&iTestingId=99393

I tried the suggestion, by running wine regedit on the prefix of the game inside the Steam folder, but it changed nothing.

This game needs the PROTON_USE_WINED3D11=1 start option to work properly, otherwise the characters are not visible. Tested with Proton 3.16-1.

Ohhh, I'll be sure to give that a go the next few days. Would be great if the game could be given a silver or gold rating, at least.

I forgot to add my specs!

Using PROTON_USE_WINED3D=1 %command% with the latest 3.16-2 beta definitely works for me and I can see all the character models, too, now.
Will have to do further playtesting, but usually if things work fine this far, they keep working.

Alright, did some more testing and with the command above, everything works just fine.
Good performance, no visual bugs.
Only the mouse seems overly sensitive, but that can be adjusted by putting it to the lowest value in the options - and that might be on Windows, too, idk.

Definitely a Gold candidate, or Platinum if the PROTON_USE_WINED3D=1 %command% came included with the game by an official whitelist.

tested on laptop ryzen 7 pro 2700U / Vega 10 (AMD RAVEN), ubuntu 18.04.1 LTS, kernel 4.19.0, mesa 19.0.0-devel, proton 3.16-2 beta
Nicely works, setting low 1024, average 30 FPS. No visual issue after 30 min gameplay (some few brutal drop fps with no apparent reason), but again works very well.