You could only use one application at a time in iPhone just because apple wanted to save its crappy battery life. After 2 years now they put push support in the OS and now today Beejive comes with Push. What push means? It means you will receive messages or stay online even though you press the home button and doing something else.
Beejive is now using their own licencing and blacklisting service so bad news for the freeloaders. Second best is the IM+ in my opinion and then the best one for mobile for long years Agile Messenger. They are both coming with PUSH support in couple of day be patient 
BeejiveIM Key Features:
- BeejiveIM uses your existing data plan: no per-message charges.
- Reliable and efficient networking: be connected 24/7, and it's gentle on your battery.
- Be connected even after you close the application. Get notified instantly when you get a new message with Push Notifications.
- Works with multiple IM networks, multiple accounts per network: AIM®/iChat, MSN®, Yahoo!®, GoogleTalk®, Facebook IM, ICQ®, Jabber, and MySpace IM.
- Send and receive files, including pictures and voice notes. View and forward received documents.
- Desktop-like instant messaging with all of your IM buddies from a single intuitive user interface.
Chatting Features:
- Real-time chats: quick switch between multiple simultaneous chats.
- Full Unicode support, chat in any language supported by your iPhone.
- Landscape option, type with a larger keyboard.
- Chat history: Email chat logs to save chat history.
- Hyperlink support, automatically parses links for web pages, YouTube videos, email addresses, and phone numbers.
- Emoticons support.
- SMS out, chat with your SMS buddies through AIM or Yahoo SMS out. SMS out is fully integrated with your iPhone/iPod Touch address book.
Account & Buddy Features:
- Manage your buddy-list, including add/remove, nicknames, groups, block, approve/deny requests.
- Merge multiple IM buddies for the same contact under a single buddy list entry with meta contacts.
- Sort/group/search your buddy list.
- Control your own availability, set auto-away and custom status messages, be invisible, change privacy controls.
- Configurable alerts, customizable sound, vibrate settings.
- Buddy icon support, view your friends' icons, set your own.