Is that what hangouts is? A WiFi messenger like imessaging
Sent from my stock Samsung Galaxy S3 - Sapphire Black
It can be messaging and/or video chat.
Hangouts is a work in progress but it does work well as a chat, and you can send pics as well. Here's some others to consider which will allow you both to keep your respective phones.
Perhaps the most popular text messaging app out there is handsent, and it's a cross-platform texting tool so it will communicate between iPhones and Android phones.
https://play.google.com/store/apps/details?id=com.handcent.nextsms
Let's not forget Skype which works across all platforms.
https://play.google.com/store/apps/details?id=com.skype.raider
Kakao is a Skype-like tool, also video and text chat for free.
https://play.google.com/store/apps/details?id=com.kakao.talk
Another one that's extremely popular is Yahoo Messenger.
https://play.google.com/store/apps/details?id=com.yahoo.mobile.client.android.imvideo
Whatsapp is very popular as well.
https://play.google.com/store/apps/details?id=com.whatsapp
Here's one that actually looks like the iPhone Instant Messaging on the Android platform, including emojis with the plug-in (second link)
https://play.google.com/store/apps/details?id=com.iphonestyle.mms
https://play.google.com/store/apps/details?id=com.iphonestyle.mms.emoji
I use TextFree (Pinger) to communicate with my son who has no cellular service but only WIFI access on my old D2. It works like a charm and is FREE texting. No, it's not true IM, but it's certainly a way to keep in touch and works on WIFI, so it would do what you want.
https://play.google.com/store/apps/details?id=com.pinger.textfree
Don't forget that Facebook has its own chat tool and is completely cross-platform.
https://play.google.com/store/apps/details?id=com.facebook.orca
I actually like Tango, which is also cross-platform and it's not only text but video as well.
https://play.google.com/store/apps/details?id=com.sgiggle.production
ooVoo is cross-platform video chat and perhaps one of the most popular of all.
https://play.google.com/store/apps/details?id=com.oovoo
Viber is very similar in many ways.
https://play.google.com/store/apps/details?id=com.viber.voip
A couple other video chat tools.
https://play.google.com/store/apps/details?id=com.c2call.app.android.friendcaller
https://play.google.com/store/apps/details?id=air.com.fbvideochat.fbvideochat
https://play.google.com/store/apps/details?id=com.camshare.camfrog.android
Mchat looks interesting.
https://play.google.com/store/apps/details?id=com.mchat
Mailtok is getting great reviews and is generating a lot of interest.
https://play.google.com/store/apps/details?id=mailtok.android
You can even have completely secure encrypted chat for those times when the messages are for "her eyes only" and vice versa...
https://play.google.com/store/apps/details?id=info.guardianproject.otr.app.im
There's also a walkie-talkie type communications tool, think of Nextel, where you push to talk. It's completely VOIP, so there's no cellular "phone call" initiated. Therefore it will work over WIFI or Cellular, and on WIFI it doesn't need a cellular connection.
https://play.google.com/store/apps/details?id=mobi.androidcloud.app.ptt.client
Voxer is another push to talk app.
https://play.google.com/store/apps/details?id=com.rebelvox.voxer
And here's a GREAT tool you can use to both communicate from PC to phone via Instant Messaging, as well as to manage and answer your own Instant Messaging right from your desktop. It's a web-based (and Chrome plug-in), app that actually uses your phone to send and receive the text messages, and lets you do so completely without ever even touching your phone. I use it as a business tool for me and it's fantastic.
https://play.google.com/store/apps/details?id=com.texty.sms
Now I may have made one or two mistakes up there, but the fact is communicating between Android and iPhone IS available, and so there's really no reason for that to be the hinge-point in your decision.