I have a Raspberry Pi 3 Model B (with Raspbian Stretch Lite installed) connected to my laptop by Ethernet using a static IP address (network: 192.168.128.0). I can access it through ssh without any problems.
Both Raspi and Laptop are connected to my home WiFi network (192.168.1.0). 
I was able to do apt-get update && apt-get upgrade and get a response when pinging sites offering an IPv6 address (google.com, www.fefe.de), but not so for IPv4 addresses (such as github.com, which is resolved as 192.30.253.112).
Why can't I communicate with IPv4 sites?
Here's what ifconfig says:
eth0: flags=4163<UP,BROADCAST,RUNNING,MULTICAST>  mtu 1500
    inet 192.168.128.66  netmask 255.255.255.0  broadcast 192.168.128.255
    inet6 fe80::ba27:ebff:fe5e:11a4  prefixlen 64  scopeid 0x20<link>
    ether b8:27:eb:5e:11:a4  txqueuelen 1000  (Ethernet)
    RX packets 0  bytes 0 (0.0 B)
    RX errors 0  dropped 0  overruns 0  frame 0
    TX packets 284  bytes 23167 (22.6 KiB)
    TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0
lo: flags=73<UP,LOOPBACK,RUNNING>  mtu 65536
    inet 127.0.0.1  netmask 255.0.0.0
    inet6 ::1  prefixlen 128  scopeid 0x10<host>
    loop  txqueuelen 1  (Local Loopback)
    RX packets 163  bytes 16590 (16.2 KiB)
    RX errors 0  dropped 0  overruns 0  frame 0
    TX packets 163  bytes 16590 (16.2 KiB)
    TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0
wlan0: flags=4163<UP,BROADCAST,RUNNING,MULTICAST>  mtu 1500
    inet 192.168.1.109  netmask 255.255.255.0  broadcast 192.168.1.255
    inet6 fe80::ba27:ebff:fe0b:44f1  prefixlen 64  scopeid 0x20<link>
    inet6 2a02:1205:506b:20d0:ba27:ebff:fe0b:44f1  prefixlen 64  scopeid 0x0<global>
    ether b8:27:eb:0b:44:f1  txqueuelen 1000  (Ethernet)
    RX packets 2862  bytes 287666 (280.9 KiB)
    RX errors 0  dropped 0  overruns 0  frame 0
    TX packets 1783  bytes 322848 (315.2 KiB)
    TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0
And here what iwconfig says:
eth0      no wireless extensions.
lo        no wireless extensions.
wlan0     IEEE 802.11  ESSID:"bucher"
      Mode:Managed  Frequency:2.437 GHz  Access Point: D0:05:2A:1B:ED:78
      Bit Rate=65 Mb/s   Tx-Power=31 dBm
      Retry short limit:7   RTS thr:off   Fragment thr:off
      Power Management:on
      Link Quality=43/70  Signal level=-67 dBm
      Rx invalid nwid:0  Rx invalid crypt:0  Rx invalid frag:0
      Tx excessive retries:0  Invalid misc:0   Missed beacon:0
And finally my /etc/network/interfaces file:
source-directory /etc/network/interfaces.d
auto eth0
allow-hotplug eth0
iface eth0 inet static
        address 192.168.128.66
        netmask 255.255.255.0
        gateway 192.168.128.1
auto wlan0
allow-hotplug wlan0
iface wlan0 inet dhcp
wpa-conf /etc/wpa_supplicant/wpa_supplicant.conf
Edit /etc/resolv.conf:
domain home
nameserver 192.168.1.1
/etc/resolv.confabove now, thanks for pointing out. Why can't I have two networks when each device has two network devices? – Patrick Bucher Oct 29 '17 at 11:16