On US15.10 I have nginx:

root@LIA-RP-VS-WEB:/etc/nginx/tls# nginx -V
nginx version: nginx/1.9.12
built by gcc 5.2.1 20151010 (Ubuntu 5.2.1-22ubuntu2)
built with OpenSSL 1.0.2d 9 Jul 2015
TLS SNI support enabled
configure arguments: --prefix=/etc/nginx --sbin-path=/usr/sbin/nginx --modules-path=/etc/nginx/modules --conf-path=/etc/nginx/nginx.conf --error-log-path=/var/log/nginx/error.log --http-log-path=/var/log/nginx/access.log --pid-path=/var/run/nginx.pid --lock-path=/var/run/nginx.lock --http-client-body-temp-path=/var/cache/nginx/client_temp --http-proxy-temp-path=/var/cache/nginx/proxy_temp --http-fastcgi-temp-path=/var/cache/nginx/fastcgi_temp --http-uwsgi-temp-path=/var/cache/nginx/uwsgi_temp --http-scgi-temp-path=/var/cache/nginx/scgi_temp --user=nginx --group=nginx --with-http_ssl_module --with-http_realip_module --with-http_addition_module --with-http_sub_module --with-http_dav_module --with-http_flv_module --with-http_mp4_module --with-http_gunzip_module --with-http_gzip_static_module --with-http_random_index_module --with-http_secure_link_module --with-http_stub_status_module --with-http_auth_request_module --with-http_xslt_module=dynamic --with-http_image_filter_module=dynamic --with-http_geoip_module=dynamic --with-threads --with-stream --with-stream_ssl_module --with-http_slice_module --with-mail --with-mail_ssl_module --with-file-aio --with-http_v2_module --with-cc-opt='-g -O2 -fstack-protector-strong -Wformat -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2' --with-ld-opt='-Wl,-Bsymbolic-functions -Wl,-z,relro -Wl,--as-needed' --with-ipv6


OpenSSL

root@LIA-RP-VS-WEB:/etc/nginx/tls# openssl version -a -v -b -o -f -p -d
OpenSSL 1.0.2g 1 Mar 2016
built on: reproducible build, date unspecified
platform: debian-amd64
options: bn(64,64) rc4(16x,int) des(idx,cisc,16,int) blowfish(idx)
compiler: gcc -I. -I.. -I../include -fPIC -DOPENSSL_PIC -DOPENSSL_THREADS -D_REENTRANT -DDSO_DLFCN -DHAVE_DLFCN_H -m64 -DL_ENDIAN -g -O2 -fstack-protector-strong -Wformat -Werror=format-security -D_FORTIFY_SOURCE=2 -Wl,-Bsymbolic-functions -Wl,-z,relro -Wa,--noexecstack -Wall -DMD32_REG_T=int -DOPENSSL_IA32_SSE2 -DOPENSSL_BN_ASM_MONT -DOPENSSL_BN_ASM_MONT5 -DOPENSSL_BN_ASM_GF2m -DSHA1_ASM -DSHA256_ASM -DSHA512_ASM -DMD5_ASM -DAES_ASM -DVPAES_ASM -DBSAES_ASM -DWHIRLPOOL_ASM -DGHASH_ASM -DECP_NISTZ256_ASM
OPENSSLDIR: "/usr/lib/ssl"

Problem with IE 11 is still exist. First connection to static page is HTTP/2 and if I do refresh I am getting HTTPS in developers tools. FF and Chrome do not have this problem.

I think (I feel, my intuition tells me :) ) it may lay on self signed certificate. I have create it following the
https://tools.ietf.org/html/rfc7540#section-9.2 requirements.

root@LIA-RP-VS-WEB:/etc/nginx/tls# openssl ecparam -out privatekey.key -name prime256v1 -genkey
root@LIA-RP-VS-WEB:/etc/nginx/tls# openssl req -new -key privatekey.key -out csr.pem
root@LIA-RP-VS-WEB:/etc/nginx/tls# openssl req -x509 -days 365 -key privatekey.key -in csr.pem -out certificate.crt
root@LIA-RP-VS-WEB:/etc/nginx/tls# ll
total 20
drwxr-xr-x 2 root root 4096 Mar 13 20:48 ./
drwxr-xr-x 4 root root 4096 Mar 13 20:45 ../
-rw-r--r-- 1 root root 899 Mar 13 20:48 certificate.crt
-rw-r--r-- 1 root root 530 Mar 13 20:48 csr.pem
-rw-r--r-- 1 root root 302 Mar 13 20:45 privatekey.key

This certificate is used for both HTTPS and HTTP2.

P.S.: I saw multiple tutorials where nginx plays a role as a simple forward proxy for HTTP and HTTPS, will it work for HTTP/2? Any Idea?