You can achieve what you want without the instanceof keyword as you can write custom type guards now:

interface A {
    member: string;
}

function instanceOfA(object: any): object is A {
    return 'member' in object;
}

var a: any = {member: "foobar"};

if (instanceOfA(a)) {
    alert(a.member);
}

Lots of Members

If you need to check a lot of members to determine whether an object matches your type, you could instead add a discriminator. The below is the most basic example, and requires you to manage your own discriminators... you'd need to get deeper into the patterns to ensure you avoid duplicate discriminators.

interface A {
    discriminator: 'I-AM-A';
    member: string;
}

function instanceOfA(object: any): object is A {
    return object.discriminator === 'I-AM-A';
}

var a: any = {discriminator: 'I-AM-A', member: "foobar"};

if (instanceOfA(a)) {
    alert(a.member);
}

It wasn't possible before but luckily it is now, since TypeScript version 2.1. It was released on the 7th of December 2016 and introduces indexed access types, also called lookup types.

The syntax looks like element access but is written in place of types. So in your case:

interface I1 {
    x: unknown;
}

interface I2 {
    y: {
        a: I1,
        b: I1,
        c: I1,
    }
    z: unknown,
}

const myVar: I2['y'];  // indexed access type

Now myVar has the type of I2.y.

Check it out in TypeScript Playground.

2019 Update

The current answers and the official documentation are outdated. And for those new to TypeScript, the terminology used isn't clear without examples. Below is a list of up-to-date differences.

 1. Objects / Functions

Both can be used to describe the shape of an object or a function signature. But the syntax differs.

Interface

interface Point {
  x: number;
  y: number;
}

interface SetPoint {
  (x: number, y: number): void;
}

Type alias

type Point = {
  x: number;
  y: number;
};

type SetPoint = (x: number, y: number) => void;

 2. Other Types

Unlike an interface, the type alias can also be used for other types such as primitives, unions, and tuples.

// primitive
type Name = string;

// object
type PartialPointX = { x: number; };
type PartialPointY = { y: number; };

// union
type PartialPoint = PartialPointX | PartialPointY;

// tuple
type Data = [number, string];

 3. Extend

Both can be extended, but again, the syntax differs. Additionally, note that an interface and type alias are not mutually exclusive. An interface can extend a type alias, and vice versa.

Interface extends interface

interface PartialPointX { x: number; }
interface Point extends PartialPointX { y: number; }

Type alias extends type alias

type PartialPointX = { x: number; };
type Point = PartialPointX & { y: number; };

Interface extends type alias

type PartialPointX = { x: number; };
interface Point extends PartialPointX { y: number; }

Type alias extends interface

interface PartialPointX { x: number; }
type Point = PartialPointX & { y: number; };

 4. Implements

A class can implement an interface or type alias, both in the same exact way. Note however that a class and interface are considered static blueprints. Therefore, they can not implement / extend a type alias that names a union type.

interface Point {
  x: number;
  y: number;
}

class SomePoint implements Point {
  x = 1;
  y = 2;
}

type Point2 = {
  x: number;
  y: number;
};

class SomePoint2 implements Point2 {
  x = 1;
  y = 2;
}

type PartialPoint = { x: number; } | { y: number; };

// FIXME: can not implement a union type
class SomePartialPoint implements PartialPoint {
  x = 1;
  y = 2;
}

 5. Declaration merging

Unlike a type alias, an interface can be defined multiple times, and will be treated as a single interface (with members of all declarations being merged).

// These two declarations become:
// interface Point { x: number; y: number; }
interface Point { x: number; }
interface Point { y: number; }

const point: Point = { x: 1, y: 2 };

You are trying to index a type with a real value, and this is not allowed. You need to access it with a type (playground):

interface T {
  a: number;
  b: string;
  c: boolean;
}

const func = <K extends keyof T>(key: K, value: T[K]) => {};

func("a", 5);
func("b", 5); // Argument of type 'number' is not assignable to parameter of type 'string'.

There is a clear distinction between types and real values in typescript since the type information is lost after transpilation. Thus you cannot use real values to define type logic. The only way would be to extract the type value of a real value (e.g., with typeof), which is why the compiler suggests transitioning your real value into a type.