You can create three nodes for one city.

In other words, You create a bus station, train station, airport in one city. If you arrive in city A with a train but leave with a plane, you have to move from the train station to Airport. And then you can assign 0 (or appropriate quantities, emission or time) for moving between any of them within the same city.

There could be a better way to formulate because the number of nodes becomes 3 times in this way.

You can create three nodes for one city.

In other words, You create a bus station, train station, airport in one city. If you arrive in city A with a train but leave with a plane, you have to move from the train station to Airport. And then you can assign 0 (or appropriate quantities, emission or time) for moving between any of them within the same city.

There could be a better way to formulate because the number of nodes becomes 3 times in this way.

And Multi-objective part, You cannot solve the problem with three objectives, like LP or MIP.

The multi-objective problem can be solved in several different ways.

1. Create one measure, You can add three numbers, with weights. for example, you can create a measure, 20% of emission + 40% of time + 40% of the cost. and then Minimize the measure.

2. Set two of them as constraints and minimize one. For example, limit the amount of emission. Total emission should be less than a certain amount. And total cost should be less than $5000. and Minimize the travel time.

3. Find Pareto optimal solutions. (Find Efficiency frontier) Find solutions that are not dominated by any other solutions. Let the decision-maker to choose the solution.

There are a lot more in detail. Take a course or read a book in "Multi-Objective Optimization"