I just subscribed to Telegram, and I discovered that for all my contacts that have both Telegram and WhatsApp, their WhatsApp entry/connection in my address book got replaced by the Telegram one, while I was expecting both would show up.
Is there anything I can do to see both of them?
Telegram will not replace Whatsapp contacts. Whatsapp doesn't store any of your contacts on its server. It just reads your address book and find matched contacts that have Whatsapp account and display them as Whatsapp associated contacts. This is different from how Telegram stores your Contacts. Telegram uploads your contact database to your account on its servers and keeps a copy of your address book on its servers. Once an address book entry is kept on its server, it gets displayed as telegram contact, even if you don't have it in your phone.
If you are unable to see WhatsApp contacts that do have Whatsapp account, then the problems appears to be Whatsapp not able to read address book. It it irrelated to having Telegram installed.
Possible solutions are:
WhatsApp > Menu Button > Settings > Chats and calls > Back up chats or Chat backup. Then uninstall Whatsapp. Reboot phone. Reinstall WhatsApp and restore chat history during account setup. Settings > Accounts, press menu button and check Auto Sync data. Also, Tap on WhatsApp and select checkbox for Contacts sync. Contacts > Menu button > Contacts to display and see if All Contacts is selected. Also go to Contacts > Menu button > Accounts and see if both WhatsApp and Telegram accounts can be seen and refreshed. 
