If you asked Oscar Pistorius, he'd tell you "not bullet proof at all".
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Barrier penetration depends on both the cartridge being used as well as the specific load/bullet used.
In wood here is some data I copy and pasted for somewhere about 15 years ago - sorry I can't recall the original source.
The loads in yellow are those that might be stopped by a 1.5" thick solid wood door (but it's very doubtful).
Plywood has a fair amount of glue in it, and each ply in the wood presents a new penetration challenge for the bullet as the wood won't just continue to split along the structure of the grain, so plywood is a lot more bullet resistant than solid wood - when the same wood is used in both applications.
As a comparative example, I've personally shot 73 gr FMJ .32 ACP rounds through 2 stacked pine 2x4s and shot 95 gr FMJ .380 ACP rounds through 3 stacked pine 2x4s. That's 3" of pine for the lowly .32 ACP and 4.5" of pine of for the .380 ACP. Having a .380 ACP shoot through 4.5" of pine, isn't a strong recommendation for solid wood doors made from pine.
Compare that 4.5" of pine with 1.8" of plywood noted below and it's an indication of how much tougher plywood is than soft pine.
Wood also varies a lot in density. A solid oak door for example will be more bullet resistant than one made of soft pine (there's a reason they used oak on ships of the line).
Bullet penetration table, inches of plywood (test blocks made up of 1/2" sheet ply).
.380 ACP (9mm Kurz)
95 grain FMJ 1.8"
85 grain Silvertip 0.9"
.38 Special
158 grain SWC 2.3"
125 grain JHP +P 1.7"
110 grain SJHP +P 1.4"
158 grain SWC-HP +P 1.3"
9mm Parabellum
123 grain FMJ 4.4"
115 grain JHP +P+ 3.0"
115 grain JHP 2.7"
115 grain Silvertip 2.5"
124 grain Nyclad 2.3"
147 grain JHP 2.0"
80 grain Glaser 2.0"
140 grain SJHP 1.7"
.357 Magnum
158 grain SWC 4.0"
145 grain Silvertip 3.0"
125 grain SJHP 2.5"
158 grain JHP 2.2"
110 grain SJHP 1.8"
.41 Magnum
210 grain JSP 3.4"
175 grain Silvertip 3.0"
.44 Magnum
185 grain JHP 3.7"
240 grain JHP 2.9"
233 grain Shot Shell 2.3"
.45 ACP
230 grain FMJ 2.8"
200 grain JHP 2.4"
185 grain JHP 2.4"
185 grain Silvertip 1.7"
135 grain Glaser 1.3"
12 Gauge Shotgun
1oz Slug 3.5"
00 Copper Shot 2.1"
000 Shot (LG) 2.1"
00 Shot (SSG) 1.9"
0 Shot 1.6"
No. 1 Shot 1.4"
No. 4 Shot 1.2"
No. 7 Shot 0.5"
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Steel is a different question with a host of different variables,a nd the mathematical models used to produce performance are pretty complicated.
Practically speaking, thin gauge mild steel used in metal residential doors isn't very bullet resistant at all and most handgun rounds 9mm Para or larger with FMJ or jacketed hollow point construction will penetrate them.
If the door has a solid wood core between the 2 mild steel plates, it might be a different story.
If on the other hand the door has 1/4" of mild steel plate, the odds of penetration with a handgun round are low.
