Why does my 4S keep splitting my text messages?
I have suffered numerous... Countless compatibility issues between different handsets/carriers. Even when texting in the same country.

One thing you have to understand is that a text is normally limited to 160 7-bits characters. Which means that any message containing special characters outside the range of the 7 bits characters will immediately be shorter.

According to Wikipedia:


  Depending on which alphabet the subscriber has configured in the handset, this leads to the maximum individual short message sizes of 160 7-bit characters, 140 8-bit characters, or 70 16-bit characters.


Depending on the characters you use the iPhone will select the character set adapted to the message.

Also I noticed that sometimes problems with character encodings and message length appeared when I was receiving messages from another carrier.

You should try sending the same message to another phone on the same carrier, then the same message on your carrier to see if the problem can be reproduced in these contexts. 



As a side note you say you have an unlimited data plan. To my knowledge no carrier includes text messages in the data plan. You might want to check if you have unlimited text messages in your plan. If you use iMessage (blue messages on the iPhone) you effectively use the data plan, otherwise (green messages) go through the voice/text plan.