whenever you are looking at the price of a pair, there is always a base currency that the other one is traded with. in case of ETH/BTC bitcoin is that base currency. think of BTC here as USD when you trade BTC/USD.
so when you say ETH/BTC price is 0.1 it means that you pay 0.1 bitcoin to get 1 Ethereum.
there is no split chart. it is one market with 1 chart.
This, the data sets you could look at if you wanted something resembling what a split chart would be would be ETH/USD and BTC/USD, viewing them against something else should show their individual price movements and how that's then reflected on the ETH/BTC chart.